Question

What is the Greatest Common Factor (GCF) for the following pairs of expressions?

A) GCF for 24 and 48m is 24
B) GCF for 32a and 48b is 16
C) GCF for 36k and 144km is 36k
D) GCF for 3x + 6 and 2x - 15 is 3x
E) GCF for 12x + 30y is 6

Answer 1

The Greatest Common Factor (GCF) for the given pairs of expressions are: A) 24, B) 16, C) 36k, D) No GCF, E) 6.

Step-by-step explanation:

The Greatest Common Factor (GCF) is the largest number that divides evenly into two or more numbers. To find the GCF, we need to find the common factors of the given numbers and determine the largest one. Let's go through each pair of expressions:

A) The common factors of 24 and 48m are 1, 2, 3, 4, 6, 8, 12, and 24. The largest common factor is 24, so the GCF is 24.

B) The common factors of 32a and 48b are 1, 2, 4, 8, 16, and 32. The largest common factor is 16, so the GCF is 16.

C) The common factors of 36k and 144km are 1, 2, 3, 4, 6, 9, 12, and 36k. The largest common factor is 36k, so the GCF is 36k.

D) The expression 3x + 6 does not have a GCF with the expression 2x - 15 because they have different variables and coefficients.

E) The common factors of 12x and 30y are 1, 2, 3, 6, and 12. The largest common factor is 6, so the GCF is 6.