Question

What is the greatest common factor of 42, 56, and 112?

A) 7
B) 14
C) 28
D) 21

Answer 1

The greatest common factor of 42, 56, and 112 is 14.

Step-by-step explanation:

To find the greatest common factor (GCF) of 42, 56, and 112, we can use the prime factorization method. Start by factoring each of the given numbers into their prime factors:

• 42 = 2 * 3 * 7
• 56 = 2^3 * 7
• 112 = 2^4 * 7

Now, identify the common prime factors among these numbers. In this case, the common prime factors are 2 and 7. To find the GCF, we take the product of the smallest exponent of each common prime factor:

GCF = 2^1 * 7^1 = 14

Therefore, the greatest common factor of 42, 56, and 112 is 14.