Question

Anthony has two ribbons. One is 12 inches long and the other is 20 inches long. He wants to cut the ribbons into smaller strips that are all equal in length. What is the greatest length he can make each strip if he wants to use all the ribbon

Answer 1

Answer:

$4$ inches.

Step-by-step explanation:

Length of first ribbon $=12$ inches.

Length of second ribbon $=20$ inches.

To find the greatest length he can make of smaller strips that are all equal in length, we need to find the H.C.F of the two numbers.

$12=2\times 2\times 3$

$20=2\times 2\times 5$

For H.C.F, we will take the product of all the common factors in the prime factorization of the two numbers.

H.C.F $=2\times 2=4$

So, he can cut three $4$ inches ribbons from the $12$ inches ribbon and five $4$ inches ribbons from the $20$ inches ribbon.

Hence, the greatest length he can make of smaller strips that are all equal in length is $4$ inches.