Question

A carpenter has two lengths of wood; one is 108cm long and the other is 72cm long. He wants to cut them up to produce smaller pieces of wood to build a shelving unit so they all need to be the same length, with no wood left over. What is the greatest length, in cm, that he can make the shelves?

Answer 1

Answer: He needs 36 cm to make the shelves.

Explanation:

Since we have given that

Length of first wood = 108 cm

Length of second wood = 72 cm

We need to find the greatest length so that he can make the shelves.

Greatest length = h.c.f. of 108 and 72 { 36 cm.

Hence, he needs 36 cm to make the shelves.

Answer 2

36 centimeters.

Explanation:

1. To solve this problem you must find the Greatest common factor.

2. List the prime factor of 108 and 72:

`108:(2)(2)(3)(3)(3)=(2^(2))(3^(3))\\ 72:(2)(2)(2)(3)(3)=(2^(3))(3^(2))`

3. Now, you must choose the common prime numbers with the lowest exponents and multiply them:

`(2^(2))(3^(2))=(4)(9)=36`