Question

3.02]What is the greatest common factor of twenty-eight and forty-two?

Answer 1

To find the greatest common factor (GCF) of two or more quantities:

1) factor each quantity into its prime factors
2) multiply together all of the common factors found, using the highest powers found in common

For example, find the GCF of 15 and 25:

\[15 = 3*5\]\[25 = 5*5 = 5^2\]

The only common factor found is \(5\), so the \(GCF(15,25)= 5\). We don't use \(5^2\) because that doesn't appear in both factorings.

Find the GCF of 12 and 36:
\[12 = 2*2*3 = 2^2*3\]\[
36 = 2*2*3*3 = 2^2*3^2\]\[GCF(12,36) = 2^2*3 = 12\]