algebra word problem

Question

A certain number of cats (more than 1) had 161 kittens. Each cat had the same number of kittens(more than 1) and each cat had fewer kittens than there were cats. Find the number of cats

Answer 1

The prime factors of 161 are 7 and 23.    Since each cat had the same number of kittens, this implies that there were either:   23 cats having 7 kittens each , or   7 cats having 23 kittens each.  Since each cat had fewer kittens than the number of cats,  this rules out the 7 cats having 23 kittens each.

 

Consequently,   there were 23 cats having 7 kittens each.