How do you find the greatest common factor of 24, 28?

Question

Riley Anderson · Accepted Answer

Find the prime factorization for both numbers and multiply all common factors.

You could find the prime factorizations of #24# and #28#. #24 = 2^2 * 3# #28 = 2^2 * 7# We see that #24# and #28# have #2^2# in common and nothing else, so the greatest common factor is #2^2 = 4# Although it is a little more time-consuming and pointless, there are alternative methods to determine the GCF, such as listing all the factors associated with each number and selecting the best one.

Zoe Adams · Answer

undefined To find the greatest common factor (GCF) of two numbers, you can use various methods such as prime factorization, listing factors, or using the Euclidean algorithm. For 24 and 28:

1. **Listing Factors Method:**
   - Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
   - Factors of 28: 1, 2, 4, 7, 14, 28
   - The common factors are 1, 2, and 4.
   - Therefore, the greatest common factor of 24 and 28 is 4.

2. **Prime Factorization Method:**
   - Prime factorization of 24: 2 × 2 × 2 × 3
   - Prime factorization of 28: 2 × 2 × 7
   - The common prime factors are 2 and 2.
   - Multiplying the common prime factors, we get 2 × 2 = 4.
   - Therefore, the greatest common factor of 24 and 28 is 4.

Therefore, the greatest common factor of 24 and 28 is 4.