Question

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?

Answer 1

She should cut it 72inches long couse that's as long as it get sorry if I spell wroug but I'm better at math than spelling

Answer 2

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
`2*2*2*3*3` or
`2^3*3^2`
For 90, the prime factors ar
`2*3*3*5` or
`2*3^2*5`
We are interested in the prime factors which are repeated. In this case, that's
`2*3*3` or
`2*3^2`

`2*3^2=2*9=18` 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.