We have been given that Judy’s brother Sam has a collection of 96 comic books. We have been asked to find the 10 ways Sam could divide his comic books into equal groups.

This can be done as follows:

96 can be written as $2\times 48=48\times 2=96$ . Thus, we can either have 2 groups of 48 comics or 48 groups of 2 comics. As we can see we have 2 ways to divide the comic books in equal groups.

Likewise, 96 can also be written as $3\times 32=32\times 3=96$ . Here, we can similarly see that we can either have 3 groups of 32 comics or 32 groups of 3 comics. As we can again see we have 2 more ways to divide the comic books in equal groups, taking the total number of ways to 4.

Continuing in this manner we will see that we can have 4 groups of 24 or 24 groups of 4, 6 groups of 16 or 16 groups of 6 and lastly 12 groups of 8 or 8 groups of 12 comic books, thus taking the count to a total of 10 ways in which Sam can divide his comic books into equal groups.

Our question has been answered.

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3 years ago