Sue is cutting a 96 inch piece of string and a 72 inch piece of string. she wants to make the cuts the same length and wants no string left over. what is the longest possible length she can cut the

You need the greatest common factor of both numbers.

First, we find the prime factors of each number.

96/2 = 48
48/2 = 24
24/2 = 12
12/2 = 6
6/2 = 3
3/3 = 1

96 = 2 * 2 * 2 * 2 * 2 * 3 = 2^5 * 3

72/2 = 36
36/2 = 18
18/2 = 9
9/3 = 3
3/3 = 1

72 = 2 * 2 * 2 * 3 * 3 = 2^3 * 3^2

Now we have the prime factorizations of 96 and 72.

The GCF of two numbers is a product of some of the prime factors of the numbers. The prime factors you choose are common factors with lower exponent.

Both 96 and 72 have 2 as a factor. Between 2^5 and 2^3 choose 2^3.
Both 96 and 72 have 3 as a factor. Between 3 and 3^2, choose 3.

GCF = 2^3 * 3 = 8 * 3 = 24

24 inches