Samantha has two pieces of cloth. one piece is 72 inches length and the other piece is 90 inches long. she want to cut both pieces into strips of equal length that are as long as possible. how long should she cut the strips?

So this question is basically asking for the highest common factor of 72 and 90.
You can work this out by looking at the prime factors of these numbers.
For 72, the prime factors are  or 
For 90, the prime factors ar  or 
We are interested in the prime factors which are repeated. In this case, that's  or 
so the highest common factor, and so the longest strips which could be cut from both 72 inches and 90 inches, is 18 inches.
I hope that helped.