Find the smallest positive whole number with exactly ten positive factors and list the factors.
1*1*1*1*1*1*1*1*1*1 = 1
You didn't say the factors had to be different.
yeah, but it is not "exactly" 10 factors either! LOL
To get exactly 10 factors, the first factors must be 1,2,3,4,5 (N>25, square of the fifth factor), or 1,2,3,4,6 (N>36).
However, the latter set gives a smaller number, namely 48, while the first set gives 60.
To find the smallest positive whole number with exactly ten positive factors, you need to understand the concept of factors. Factors are the whole numbers that divide a given number without leaving any remainder. The number of factors of a given number can be found by prime factorizing the number.
In this case, to find the smallest positive whole number with exactly ten positive factors, we need to look for a number that can be expressed as a product of prime numbers raised to certain powers.
The prime factorization of a number will be in the form:
n = p1^a * p2^b * p3^c * ...
For a given number to have exactly ten factors, it means that the exponent of each prime number in its prime factorization must be either 1 or 2. This is because the total number of factors of a number can be obtained by adding one to each exponent and multiplying them together.
So, let's try to find the smallest positive whole number that meets these conditions:
Start by considering a prime number raised to the power of 1: 2^1 = 2
Next, consider another prime number raised to the power of 1: 3^1 = 3
Now, multiply the two prime factors together: 2 * 3 = 6 (this is the smallest possible number with 2 prime factors)
To obtain additional factors, we can raise one of the prime factors to the power of 2, resulting in:
2^2 * 3^1 = 12
Thus, the smallest positive whole number with exactly ten positive factors is 12. The factors of 12 are: 1, 2, 3, 4, 6, 12.