What is the GCF of 28 and 42?

To determine the greatest common factor (GCF) of 28 and 42, we need to identify the factors of each number and find the largest factor that they share.

First, we can find the prime factorization of both numbers:

• The prime factorization of 28 is 2 × 2 × 7, which is expressed as (2^2 \cdot 7^1).

• The prime factorization of 42 is 2 × 3 × 7, which is expressed as (2^1 \cdot 3^1 \cdot 7^1).

Next, we find the common prime factors and their lowest powers. The common prime factors of 28 and 42 are 2 and 7.

• For the factor 2, the lowest power between (2^2) from 28 and (2^1) from 42 is (2^1).

• For the factor 7, both numbers have it as (7^1).

Now, we multiply the lowest powers of each common factor to find the GCF:

[

GCF = 2^1 \cdot 7^1 = 2 \cdot