Question

Latisha has two pieces of ribbon she plans

Answer 1

The greatest possible length of each  piece is 16 inches

Solution:

Latisha has two pieces of ribbon. One piece of ribbon is 48 inches and  the other is 80 inches

Ribbon is to be cut into pieces of equal length

To find the greatest possible length of each piece, we have to find greatest common divisor of 48 and 80

The greatest common factor, or GCF, is the greatest factor that divides two numbers

Steps to find G.C.F of 48 and 80

1) Find the prime factorization of 48

$48 = 2 \times 2 \times 2 \times 2 \times 3$

2) Find the prime factorization of 80

$80 = 2 \times 2 \times 2 \times 2 \times 5$

3) To find the GCF, multiply all the prime factors common to both numbers:

Therefore, $GCF = 2 \times 2 \times 2 \times 2 = 16$

So, 16 inches is the greatest possible length to cut so that every piece is of equal length.