Question

Zubin has two pieces of string. One piece is 36 inches long and the other is 48 inches long. He wants to cut them into equal pieces that are as long as possible. Into what lengths should he cut the strings?

Answer 1

12 pieces each:

`S_1 = 3\ in`

`S_2= 4\ in`

Explanation:

Given

`S_1 = 36\ in` -- first string

`S_2 = 48\ in` --- second string

Required

Determine the number of equal pieces

To do this, we first calculate the HCF of the length of both pieces
`(36\ and\ 48)`

`36 = 2 * 2 * 3 * 3`

`48 = 2 * 2 * 2 * 2 * 3`

`Common\ prime\ factors = 2, 2\ and\ 3`

The HCF is:

`HCF = 2 * 2 * 3`

`HCF = 12`

Hence, he can cut both strings to 12 pieces each

Recall that

`S_1 = 36\ in`

The first string can then be cut in to 3 inches each (i.e. 36/12)

`S_2 = 48\ in`

The first string can then be cut in to 4 inches each (i.e. 48/12)