How do you find the greatest common factor of 88, 55?

To find the greatest common factor (GCF) of 88 and 55, you can use the method of prime factorization or the Euclidean algorithm. Here’s a simple breakdown of both methods:

Method 1: Prime Factorization

First, we need to find the prime factors of each number:

• 88: The prime factors are 2 × 2 × 2 × 11 (or 2³ × 11).
• 55: The prime factors are 5 × 11.

Next, identify the common factors. The only common prime factor is 11. Thus, the GCF of 88 and 55 is:

GCF = 11

Method 2: Euclidean Algorithm

This method involves a series of divisions:

1. Divide 88 by 55, which gives a quotient of 1 and a remainder of 33.
2. Next, divide 55 by 33, resulting in a quotient of 1 and a remainder of 22.
3. Then, divide 33 by 22, yielding a quotient of 1 and a remainder of 11.
4. Finally, divide 22 by 11, which gives a quotient of 2 and a remainder of 0.

When the remainder reaches 0, the last non-zero remainder is the GCF. Therefore, the GCF of 88 and 55 is:

GCF = 11

In both methods, we find that the greatest common factor of 88 and 55 is 11.