Question

A carpenter has boards of lengths 24, 36, and 42 inches that must be cut into smaller boards of equal length, with no

scrap wood left over.
What is the longest length of boards he can cut?
2 inches
4 inches
6 inches
12 inches

Answer 1

The longest length of boards he can cut is 6 inches

Explanation:

Topic: HCF

Given.

Length of wood = 24, 36, and 42

To get the longest length of boards he can cut, we need to find the HCF (highest common factor) of the three measurements.

This is done as follows:

Step 1:

What number can divide 24, 36 and 42? 2

By dividing each number by 2, we have

2 || 24 --- 36 --- 42 becomes

---|| 12 ---- 18 ----- 21

Step 2:

What number can divide 12, 18 and 21? 3

2 || 24 --- 36 --- 42

3 || 12 ---- 18 ----- 21

-- || 4 ----- 6 ------- 7

Step 3;

What number can divide 4,6 and 7? None.

So the HCF is 2 * 3

HCF = 6.

Hence, the longest length of boards he can cut is 6 inches

Answer 2

6 inches

Explanation:

Highest common factor (H.C.F) usually works when we have to find the largest number that divides a specific data set. Since the question asks to determine the longest length of boards, I have to use H.C.F of 24, 36, 42:

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

42 = 2 x 3 x 7

The H.C.F of the given length of boards is = 2 x 3 = 6.

Since, we can find 2 and 3 one time from the above multiples of 24, 36, and 42.

Therefore, the longest length of boards he can cut is 6 inches.