Find the GCF of the numbers using an appropriate method.
240, 10,000, and 4500
Find the prime factorization of the number, and write it in exponent form.
670
Find the LCM for the given numbers by an appropriate method.
24, 54, and 27
240 = 2x2x2x3x5
10000 = 2x2x2x2x5x5x5x5x5
4500 = 2x2x3x3x5x5x5
HCF = 2x2x5 = 20
(2x2x5) is the longest string of multipliers that appears in all 3 numbers.
670 = 2x5x67
24=2x2x3x3
54 = 2x3x3x3
27 = 3x3x3
LCM = 2x2x3x3x3 = 108
(write down the longest string of factors you see.
Look at your other numbers and include any factors not already listed)
To find the greatest common factor (GCF) of the numbers 240, 10,000, and 4500, we can use the prime factorization method. Here's how you can do it:
1. Start by finding the prime factorization of each number:
- Prime factorization of 240: 2^4 * 3 * 5
- Prime factorization of 10,000: 2^4 * 5^4
- Prime factorization of 4500: 2^2 * 3^2 * 5^3
2. Identify the common prime factors among the numbers. In this case, the common prime factors are 2, 3, and 5.
3. Compute the GCF by taking the smallest exponent for each common prime factor:
- GCF = 2^2 * 3^1 * 5^1 = 60
Therefore, the greatest common factor of 240, 10,000, and 4500 is 60.
To find the prime factorization of the number 670 and write it in exponent form, follow these steps:
1. Start by dividing the number by the smallest prime number, which is 2. If the number is divisible by 2, divide it by 2 repeatedly until it is no longer divisible. In this case, 670 is not divisible by 2.
2. Move on to the next prime number, which is 3. Divide the number by 3 if it is divisible. In this case, 670 is not divisible by 3.
3. Continue this process with the next prime numbers until you reach the square root of the number. The next prime number is 5. Divide 670 by 5, and you get 134.
4. Repeat the process with prime numbers until you reach 1: 134 is divisible by 2 as 134/2 = 67.
5. 67 is a prime number. Since it cannot be divided further, the prime factorization of 670 is 2 * 5 * 67.
Writing it in exponent form:
670 = 2^1 * 5^1 * 67^1
To find the least common multiple (LCM) of the numbers 24, 54, and 27, you can use the prime factorization method. Here's how:
1. Find the prime factorization of each number:
- Prime factorization of 24: 2^3 * 3
- Prime factorization of 54: 2 * 3^3
- Prime factorization of 27: 3^3
2. Write down all the prime factors with the highest exponent from all the numbers:
- LCM = 2^3 * 3^3 = 8 * 27 = 216
Therefore, the least common multiple of 24, 54, and 27 is 216.