Question

Mr. Deets is making an array to display 9 pictures. For each pair of different factors, there are two arrays he can make. How many different arrays can Mr. Deets make ? Is the number of arrays odd or even Explain.

Answer 1

4 arrays,

Number of arrays is even.

Explanation:

∵ The possible pairs of two numbers which give 9 after multiplication,

( 3, 3) and (9, 1),

So, the possible array would be,

3 × 3, 9 × 1

Note : 9 × 1 can also be written as 1 × 9,

According to the question,

For each pair of different factors, there are two arrays,

3 × 3 and 9 × 1 are two arrays with no same factor,

Hence, the total arrays = 2 × 2 = 4

Which is an even number.

Answer 2

3 arrays - 1 x 9 (or 9 x 1) and 3 x 3

Hence, the number of arrays = 2 x 2 = 4 = even

First, we pair the different factors of 9.

The different factors of 9 are:

(1, 9) and (3, 3)

For each pair, Mr. Deets can make 2 arrays.

So, the total number of arrays that Mr. Deets can make = 2 x 2 = 4 and hence the number of arrays is even.