# What is the least positive integer that has exactly thirteen factors?

14,323 results
1. ## math

1)The function f is defined by the equation f(x)+ x-x^2. Which of the following represents a quadratic with no real zeros? A)f(x) +1/2 B)f(x)-1/2 C)f(x/2) D)f(x-1/2) 2) If I^(2k) = 1, and i = radical -1, which of the following must be true about k? A) k is

2. ## Math

Prove that a^3 ≡ a (mod 3) for every positive integer a. What I did: Assume a^3 ≡ a (mod 3) is true for every positive integer a. Then 3a^3 ≡ 3a (mod 3). (3a^3 - 3a)/3 = k, where k is an integer a^3 - a = k Therefore, a^3 ≡ a (mod 3). Is this a

3. ## Math

All of the following can be the product of a negative integer and positive integer EXCEPT A) 1 B) -1 C) -2 D -4 E) -6

4. ## math

U= { all positive integer less than or equal to 30} M={all even positive numbers less than or equal to 20} N={all odd number less than or equal to 19} S={all integer x: 10

5. ## math , probability

Let X and Y be two independent and identically distributed random variables that take only positive integer values. Their PMF is px (n) = py (n) = 2^-n for every n e N, where N is the set of positive integers. 1. Fix at E N. Find the probability P

6. ## Math

Tell whether the difference between the two integers is always, sometimes, or never positive. 1)Two positive integers. Never 2)Two negative integers. Sometimes. 3)A positive integer and a negative integer. Sometimes. 4)A negative integer and positive

7. ## Social Studies

"We must all hang together, or assuredly we shall all hang separately -Benjamin Franklin what message was franklin trying to convey to the second continental congress when he spoke these words? A. The thirteen colonies should make peace with Great Britain

8. ## Math

is this statement always, sometimes, or never true: the absolute value of a positive integer is a negative integer. i think never am i correct

9. ## maths

What is the smallest positive integer with exactly 12 (positive) divisors?

10. ## math

Which statement is true? A.The sum of two positive integers is sometimes positive, sometimes negative. B.The sum of two negative integers is always negative. C.The sum of a positive integer and a negative integer is always positive. D.The sum of a positive

11. ## Math

Explain how you can determine the sign of the sum of two integers if one integer is positive and the other integer is negative.

12. ## Algebra 1 Polynomials

Suppose n is an integer. Select all statements below that are true: (choose 3) A) n^2 + n is always an even integer*** B) n^2 + n is always an even integer when n is even*** C) n^2 + n is always an even integer when n is odd*** D) n^2 + n is never an even

13. ## Math

When you add a positive integer and a negative integer, you sometimes get a negative result and sometimes get a positive result. Is the same true when you multiply a positive integer and a negative integer?

14. ## math

Show that any positive odd integer is of the form 6q+1, 6q+3 or 6q+5, where q is any positive integer

15. ## Algebra 2

Let (x) be defined for all positive integer values of x as the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)?

16. ## algebra

Find two consecutive positive integers such that the sum of their squares is 85. n^2+(n+1)^2+2n = 85 n^2+n^2+2n+1=85 2n^2+2n=84 n^2+n=42 n^2+n-42=0 (n-6)(n+7)=0 n=6 n=-7 Is my work and answer correct? -7 is not a positive integer. Your first equation is

17. ## maths

can you answer this question: prove that a number 10^(3n+1), where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. with out using this method at all ................................. We will examine the sum of

18. ## math

how often does a leap year occur? what are al the prime numbers less then 12. what is the eighth multiple of 32? is the last digit of the multiples if 4 odd or even? what are the six factors of 12? what are the factors of 16. two factors of 20 are 1 and

19. ## Math

If a positive two-digit integer is divided by the sum of its digits, the quotient is 2 with a remainder of 2. What is the two-digit integer?

20. ## Algebra 2 ..

Please explain on how to do each of these! *Let (x) be defined for all positive integer values of xas the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)? Someone says that it is f(5)= 20x10x2x4=1600 I DO NOT GET

21. ## geometry

A smooth partition of the integer n is a set of positive integers a1,a2,…ak such that 1. k is a positive integer, 2. a1≤a2≤⋯≤ak, 3. ∑ki=1ai=n, and 4. ak−a1≤1. Determine how many smooth partitions there are of the integer 250.

22. ## Algebra

A positive integer minus a positive integer is always positive. This statement is sometimes true. For example, 17 – 5 = 12, but 15 – 20 = –5. post five other statements about the addition and subtraction of positive and negative integers, and ask

23. ## math

Let’s agree to say that a positive integer is prime-like if it is not divisible by 2, 3, or 5. How many prime-like positive integers are there less than 100? less than 1000? A positive integer is very prime-like if it is not divisible by any prime less

24. ## math

show that any positive odd integer is of the form 6q+1, 6q+3 or 6q+5, where q is any positive integer.

25. ## Math easy HELP

Written as the product of its prime factors, 360=2^3 times 3^2 times 5. So find the smallest positive integer k such that 360k is a cube number.

26. ## Math

The squares of three positive integers are in arithmetic progression, and the third integer is 12 greater than the first. Find the second integer.

27. ## writing

Combines the pairs of sentences below into compound sentenvces three different ways. Punctuate correctly. One pair of sentences should not be joined because the ideas are not related. So can you tell me if the sentences are correct. I have to use a fanboy,

28. ## Maths

Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx

29. ## Algebra

If a positive two-digit integer is divided by the sum of its digits, the quotient is 2 with a remainder of 2. What is the two-digit integer?

30. ## math

Which of these is a rational number A.)integer 150 B.)integer 441 C.)integer 200**** D.)integer 250

31. ## MATH

Find the only positive integer whose cube is the sum of the cubes of three positive integers immediately preceding it. Find this positive integer. Your algebraic work must be detailed enough to show this is the only positive integer with this property

32. ## math

For a positive integer x, let f(x) be the function which returns the number of distinct positive factors of x. If p is a prime number, what is the minimum possible value of f(75p2)?

33. ## Algebra 2.....

*Please explain on how to do each of these! 1. Let (x) be defined for all positive integer values of x as the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)? Someone says that it is f(5)= 20x10x2x4=1600 I DO NOT

34. ## ALGEBRA 2...

*Please explain on how to do each of these! 1. Let (x) be defined for all positive integer values of x as the product of all even factors of 4x. For example, (3)=12x6x4x2=576. What is the value of (5)? Someone says that it is f(5)= 20x10x2x4=1600 I DO NOT

35. ## Math

A smooth partition of the integer n is a set of positive integers a 1 ,a 2 ,…a k such that 1. k is a positive integer, 2. a 1 ≤a 2 ≤⋯≤a k , 3. ∑ k i=1 a i =n, and 4. a k −a 1 ≤1. Determine how many smooth partitions there are of the integer

36. ## Math

Paulo withdraws the same amount from his bank account each week to pay for lunch. Over the past four weeks, he withdrew one hundred twenty dollars. Which rule best applies to determine the change in his account each week? 1. The product of two positive

37. ## math

Rich chooses a 4-digit positive integer. He erases one of the digits of this integer. The remaining digits, in their original order, form a 3-digit positive integer. When Rich adds this 3-digit integer to the original 4-digit integer, the result is 6031.

38. ## Discrete Math

1. Assume that n is a positive integer. Use the proof by contradiction method to prove: If 7n + 4 is an even integer then n is an even integer. 2. Prove: n is an even integer iff 7n + 4 is an even integer. (Note this is an if and only if (iff) statement.

39. ## math

If n is a positive integer, then what is the value of (2/3)^n (1 1/2)^n-1? for positive integer n? Express your answer as a common fraciton?

40. ## mathematics

It can be shown that for any positive integer n, the infinitely nested radical expression (n+(n+(n+....)^1/2)^1/2)^1/2 equals a finite number. What is the largest positive integer n≤999 such that this expression is equal to a positive integer? Details

41. ## math

Find the smallest positive whole number with exactly ten positive factors and list the factors.

42. ## Discrete Math

Let n be positive integer greater than 1. We call n prime if the only positive integers that (exactly) divide n are 1 and n itself. For example, the first seven primes are 2, 3, 5, 7, 11, 13 and 17. (We should learn more about primes in Chapter 4.) Use the

43. ## Math (Complex Numbers)

Let N be the sum of all prime powers that can be written as 4^n+n^4 for some positive integer n. What are the last 3 digits of N? Details and assumptions: A prime power is a number of the form pk, where p is a prime and k is a positive integer. Examples:

44. ## math, algebra

2a+2ab+2b I need a lot of help in this one. it says find two consecutive positive integers such that the sum of their square is 85. how would i do this one i have no clue i know what are positive integers.but i don't know how to figure this out. Let n be a

45. ## math

Show that any positive integer is of the form 4q, 4q+2, where q is any positive integer.

46. ## math

show that any positive integer is of the form 4q, 4q+2, where q is any positive integer.

47. ## maths

the non- decreasing sequence of odd integers {a1, a2, a3, . . .} = {1,3,3,3,5,5,5,5,5,...} each positive odd integer k appears k times. it is a fact that there are integers b, c, and d such that, for all positive integers n, añ = b[√(n+c)] +d. Where [x]

48. ## PSY

I am to describe the central themes and stategies of positive psychology as I understand it. Did I understand it correct? The central themes and strategies of positive psychology recognize the importance of building positive qualities in people. It helps

49. ## Discrete Math

Theorem: For every integer n, if x and y are positive integers with max(x, y) = n, then x = y. Basic Step: Suppose that n = 1. If max(x, y) = 1 and x and y are positive integers, we have x = 1 and y = 1. Inductive Step: Let k be a positive integer. Assume

50. ## math

What ordered pair of positive integers (r, s) satisfies the equation 5r + 6s = 47, such that r > s? What is the integer for r ? What is the integer for s?

51. ## math

can you answer this question in a different and more logical way than this method below: we will examine the sum of cubes of two numbers, A and B. Without losing generality, we will further assume that A=2nX and B=2n+kY where X is not divisible by 2 n is a

52. ## Math

When the digits of a positive integer are written in reverse to form a new positive integer with the same number of digits(e.g., 1234 4321), the new number is 90 less than the original. What is the smallest possible value of the original number?

53. ## math

Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx

54. ## algebra

Find the sum of all positive integers c such that for some prime a and a positive integer b, a^b+b^a=c^a.

55. ## heeeelp math

For each positive integer n, let Hn=1/1 + 1/2 +⋯+ 1/n . If ∑ (up)∞ (base)(n=4) 1/n*Hn*H(n-1)= a/b for relatively prime positive integers a and b, find a+b.

56. ## discrete math

Prove by contradiction that for any even integer a and any odd integer b, 4 does not divide (a^2 + 2b^2). Proposition: That 4k (k is any integer) = a^2 +2b^2, and a is even, and b is odd. But 4k is even (product of any integer and 4), so a^2 must be even,

57. ## Math

If a positive two-digit integer is divided by the sum of its digits, the quotient is 2 with a remainder of 2. If the same two-digit integer is multiplied by the sum of its digits, the product is 112. What is the two-digit integer?

58. ## Math

Here is the question: Choose a nonzero integer for n to show that -n can be evaluated as a positive number. Here is my answer: If n=-2 then -n=-(-2)=2 Two negatives make a positive. Is this correct.

59. ## Math

A two-player game is played with two piles of stones, with sizes m,n. On a player's turn, that player can remove any positive integer number of stones from one pile, or the same positive integer number of stones from each pile. A player loses when they are

60. ## calculus

A positive multiple of 11 is good if it does not contain any even digits in its decimal representation. (a) Find the number of good integers less than 1000. (b) Determine the largest such good integer. (c) Fix b ≥ 2 an even integer. Find the number of

61. ## proof by mathematical induction

subject is PreCalulus. 2^(k+3) = and < (k+3)! i know how to do proving using mathematical induction when its just an equal sign, but I don't understand what to do when its an inequality. thank you!!! Here is what I would do Step 1: check if it is true for

62. ## English 10

Which sentence correctly punctuates a nonessential appositive phrase? A. Aries, one of thirteen constellations in the Zodiac, contains four stars. B. Aries one of thirteen constellations in the Zodiac contains four stars. C.Aries, one of thirteen

63. ## math

What is the least positive integer that has exactly thirteen factors?

64. ## Calculus

What is the least positive integer that has exactly thirteen factors?

65. ## Math

x^2+x-k find all positive values for k, if it can be factored Allowed values of k for for the expression to be factorable with integers are a*(a+1) where a is an integer equal to 1 or more. For example: 2, 6, 12, 20... The factors are (x-a)(x+a+1) There

66. ## algebra

For a positive integer x, let f(x) be the function which returns the number of distinct positive factors of x. If p is a prime number, what is the minimum possible value of f(75p2)?

67. ## math

For a positive integer x, let f(x) be the function which returns the number of distinct positive factors of x. If p is a prime number, what is the minimum possible value of f(75p^2)?

68. ## pcm

For positive integer x, let f(x) be the function which returns the number of distinct positive factors of x. If p is a prime number, what is the minimum possible value of f(75p2)?

69. ## DISCRETE MATHS

We need to show that 4 divides 1-n2 whenever n is an odd positive integer. If n is an odd positive integer then by definition n = 2k+1 for some non negative integer, k. Now 1 - n2 = 1 - (2k+1)2 = -4k2-4k = 4 (-k2-4k). k is a nonnegative integer, hence

70. ## MATH

Let’s agree to say that a positive integer is prime-like if it is not divisible by 2, 3, or 5. How many prime-like positive integers are there less than 100? less than 1000? A positive integer is very prime-like if it is not divisible by any prime less

71. ## MAth

In a set of five consecutive positive even integers, the ratio of the greatest integer to least integer is 2 is to 1. If these integers are arranged from lowest to highest, which is the middle integer in the list?

72. ## English

If I'm writing about the Thirteen Colonies in my paper. Does Thirteen Colonies need to be capitalized. example The Learner will develop a understanding of the three different regions in the thirteen colonies.

73. ## math, integers

State if this statement is always, sometimes, or never true. Use examples to explain. “The result of subtracting a negative integer from a negative integer is a positive integer.”

74. ## Math 7 Help!

1. negative integer is less than positive integer somtimes, always or never My answer/think: sometimes 2. A negative integer is less than another negative integer somtimes, always or never My answer/think: sometimes 3. Absolute value is the number of

75. ## arithmetic

Find the smallest positive integer P such that the cube root of 400 times P is an integer.

76. ## Math

Given a fixed positive integer k > 1, find all integer solutions to the equation y^k = x^2 + x. (x^y means x to the power of y)

77. ## math

if a lesser integer is being subtracted from a greater integer, is the answer positive or is it negative?

78. ## math

35. If b is a positive integer less than 400 and more than 100, then how many integer pairs (a,b) satisfy the equation a/b=2/9?

79. ## math

if a greater integer is being subtracted from a lesser integer, is the answer positive or negative?

80. ## Number theroy

What is the 50th smallest positive integer that can be written as the sum of distinct non-negative integer powers of 3?

81. ## math

1. If b is positive integer less than 200, then how many integer pairs (a,b) satisfy the equation a/b= 2/9?

82. ## math

1. If b is a positive integer than 200, then how many integer pairs (a,b) satisfy the equation a/b= 2/9

83. ## Math

For how many values of n where n is a positive integer less than 10 is n+1/2 an integer? A) None B) One C) Three D) Four E) Five Please I would like some help explaining how to get the answer :)

84. ## maths

prove that any odd positive integer of 8q+1,where q is any integer?

85. ## math

You are given a positive integer such that when the integer is divided by 1995, the remainder is 75. What will the remainder be when the same positive integer is divided by 57?

86. ## math

Lisa is thinking about two positive integers. The larger integer is seven less than twice the smaller integer. The larger integer is also three more than the smaller integer. What is the larger of the two integers that Lisa is thinking about? ~So the

87. ## pls heeelp math

For each positive integer n, let H _{n} = 1/1 +1/2 +⋯+ 1/n sum_{n=4}^{∞} 1/n*H_{n}*H_{n-1}=a/b for relatively prime positive integers a and b, find a+b

88. ## Maths

Suppose a and b are positive integers satisfying 1≤a≤31, 1≤b≤31 such that the polynomial P(x)=x3−ax2+a2b3x+9a2b2 has roots r, s, and t. Given that there exists a positive integer k such that (r+s)(s+t)(r+t)=k2, compute the maximum possible value

89. ## discrete math

Could someone help me with this induction proof. I know its true. given then any integer m is less than or equal to 2, is it possible to find a sequence of m-1 consecutive positive integers none of which is prime? explain any help is greatly appreciated

90. ## Proofs and numbers

Prove the following theorem: Suppose p is a prime number, r, s are positive integers and x is an arbitrary integer. Then we have x^r identical to x^s (mod p) whenever r is identical to s (mod 11).for x belongs to an integer

91. ## math

Find the sum of the first one thousand positive integers. Explain how you arrived at your result. Now explain how to find the sum of the first n positive integers, where n is any positive integer, without adding a long list of positive integers by hand and

92. ## math

An integer is 5 more than another integer. Three times the bigger integer is 11 more than the square of the smaller integer. find the two integers

93. ## Math (algebra)

For every positive integer n, consider all monic polynomials f(x) with integer coefficients, such that for some real number a x(f(x+a)−f(x))=nf(x) Find the largest possible number of such polynomials f(x) for a fixed n

94. ## math

what is the least positive integer with exactly 10 factors?

95. ## math

Given x^2 = y + a and y^2 = x + a where a is a positive integer, find expressions for that yield integer solution for x and y.

96. ## English expression

Who are teenagers? They are young people who are from thirteen to nineteen. Look at the words such as thirteen, fourteen....nineteen. They all have teen, so people who are from thirteen to nineteen are called teenagers.

97. ## English

A Thirteen Letter Word That Means "A Whole Bunch". The Thirteen Letters Are As Follows: NOSOREGGTIACN

98. ## Math (algebra)

Suppose a and b are positive integers satisfying 1≤a≤31, 1≤b≤31 such that the polynomial P(x)=x^3−ax^2+a^2b^3x+9a^2b^2 has roots r, s, and t. Given that there exists a positive integer k such that (r+s)(s+t)(r+t)=k^2, compute the maximum possible

99. ## Psychology

Sam’s I.Q. was 105 when he was tested at age nine. When he was thirteen, he was re-tested and his I.Q. was 120. Explain the increase in I.Q. using the concepts of trends/theories and socioeconomic factors.

100. ## English

e.g. In 2013, they got married. (How do you read '2013' in this sentence? 1. two thousand thirteen 2. twenty thirteen Are both acceptable? Which one is commonly used?)