Jazmyn has some strips of cloth she found for her project. The widths of the different strips are 72 cm, 96 cm, and 128 cm. They are to be cut into smaller pieces. Determine the greatest possible width of each piece so that they are all the same width.

Answer 1

To determine the greatest possible width of each piece, we need to find the greatest common divisor (GCD) of the widths of the cloth strips.

The prime factorization of 72 is $2^3 \cdot 3^2$,
the prime factorization of 96 is $2^5 \cdot 3^1$,
and the prime factorization of 128 is $2^7$.

To determine the GCD, we take the smallest power of each prime factor that appears in all three numbers:
$2^3 \cdot 3^1 = 8 \cdot 3 = 24$

So, the greatest possible width of each piece is 24 cm.