Question

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 string?!?

Answer 1

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

Answer: 24 inches