Question

What is the greatest common factor of 88 and 40?

Answer 1

To find the greatest common factor (GCF) of 88 and 40, we can use the method of prime factorization.

First, we find the prime factorization of both numbers.

**For 88:**
- 88 can be divided by 2: \( 88 \div 2 = 44 \)
- 44 can be divided by 2: \( 44 \div 2 = 22 \)
- 22 can be divided by 2: \( 22 \div 2 = 11 \)
- 11 is a prime number.

So, the prime factorization of 88 is:
\[
88 = 2^3 \times 11
\]

**For 40:**
- 40 can be divided by 2: \( 40 \div 2 = 20 \)
- 20 can be divided by 2: \( 20 \div 2 = 10 \)
- 10 can be divided by 2: \( 10 \div 2 = 5 \)
- 5 is a prime number.

So, the prime factorization of 40 is:
\[
40 = 2^3 \times 5
\]

Now, we identify the common prime factors and their lowest powers:
- The common prime factor is \( 2 \), and the lowest power is \( 2^3 \).

Therefore, the GCF of 88 and 40 is:
\[
\text{GCF} = 2^3 = 8
\]

Thus, the greatest common factor of 88 and 40 is \(\boxed{8}\).