Question

Find the greatest common factor (GCF) of 22ab^2c^2 and 40a^3c^2.

A. 4ac^2
B. 2ab^2c^2
C. 2ac^2
D. 4a^3b^2c^2

Answer 1

The GCF of 22ab^2c^2 and 40a^3c^2 is found by multiplying the lowest powers of common prime factors. The GCF is 2ac^2, which corresponds to option C.

Step-by-step explanation:

To find the greatest common factor (GCF) of 22ab2c2 and 40a3c2, we need to break down each term into its prime factors and then multiply the lowest powers of common factors.

• 22ab2c2 = 2 × 11 × a × b × b × c × c
• 40a3c2 = 2 × 2 × 2 × 5 × a × a × a × c × c

The common factors are 2, a, c2. The lowest power of 2 is just 2, for a it's a, and for c2 it's c2. Therefore, the GCF is 2ac2.

Based on the options provided, the correct answer is C. 2ac2.