Solve problems using multiples and factorsUsing factors

Here is another example of a word-based question:

Hamish works at a storage facility. They only accept cube-shaped boxes with a side of 1m. On Tuesday Hamish is expecting a delivery of 48 boxes. His manager wants the boxes to be placed against a wall and neatly arranged in the form of a rectangle. Hamish arranges them so they are 1 box high and 48 boxes long (1 x 48 = 48). In how many ways can Hamish stack the 48 boxes in rectangular form?

To answer this question follow the same process as before:

1. Highlight the key information:

Hamish works at a storage facility. They only accept cube-shaped boxes with a side of 1m. On Tuesday Hamish is expecting a delivery of 48 boxes. His manager wants the boxes to be placed against a wall and neatly arranged in the form of a rectangle. Hamish arranges them so they are 1 box high and 48 boxes long (1 x 48 = 48). In how many ways can Hamish stack the 48 boxes in rectangular form?

This problem involves factors. To create all the different rectangles you need to find factor pairs that make 48.

2. Organise the key information:

• I need to find out how many different ways there are to stack 48 boxes as a rectangle.

3. Use that information to work out the answer to the question:

(To tackle this problem we must list all of the pairs of factors of 48)

1. 1 x 48
2. 48 x 1
3. 2 x 24
4. 24 x 2
5. 3 x 16
6. 16 x 3
7. 4 x 12
8. 12 x 4
9. 6 x 8
10. 8 x 6