Brandon has 32 stamps. He wants to display the stamps in rows, with the same number of stamps in each row. How many different ways can he display the stamps? Please help answer and explain

2 and 16

4 and 8

Thanks

How do you do that can you send me a screen shot so I am get the answer

To determine the number of different ways Brandon can display the 32 stamps in rows, we can consider the factors of 32. Since each row should have the same number of stamps, the number of stamps in each row must be a factor of 32.

The factors of 32 are: 1, 2, 4, 8, 16, and 32.

Therefore, Brandon can display the stamps in the following ways:
- One stamp per row: Only one way to arrange them.
- Two stamps per row: Divide the 32 stamps into 16 pairs, which can be arranged in 16! (factorial) ways. However, since the pairs are identical, we need to divide by 2! for each pair. Hence, there are 16! / (2!^16) ways to arrange them.
- Four stamps per row: Divide the 32 stamps into 8 groups of 4. We can rearrange these groups in 8! ways, but each group is identical, so we divide by 4! for each group. Therefore, there are 8! / (4!^8) ways.
- Eight stamps per row: Divide the 32 stamps into 4 groups of 8. We can rearrange these groups in 4! ways, but each group is identical, so we divide by 8! for each group. Hence, there are 4! / (8!^4) ways.
- Sixteen stamps per row: Divide the 32 stamps into 2 groups of 16. Since there are only two groups, the number of ways is simply 2! = 2.

Adding up all the different arrangements, we get:
1 + 16! / (2!^16) + 8! / (4!^8) + 4! / (8!^4) + 2 = 1 + 77520 + 70 + 1 + 2 = 77694 different ways for Brandon to display the stamps in rows.