SOLUTION: Charu and shanaya have ribbons of 72 cm each. They cut their ribbons completely into strips of equal lengths. But they choose different lengths for making the strips. Can you find

Question 1003764: Charu and shanaya have ribbons of 72 cm each. They cut their ribbons completely into strips of equal lengths. But they choose different lengths for making the strips. Can you find out the possible lengths in which they might have cut the ribbons?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
assuming that each strip has to be an integer, then the possible ways they can cut their ribbon into equal strips would be:

1 * 72
2 * 36
3 * 24
4 * 18
6 * 12
8 * 9
9 * 8
12 * 6
18 * 4
24 * 3
36 * 2
72 * 1

the first number is the number of strips and the second number is the length of each strip.

if you look at all of the prime factors of 72, you will get:

1 * 72 = 2 * 36 = 2 * 2 * 18 = 2 * 2 * 2 * 9 = 2 * 2 * 2 * 3 * 3

every one of the options above will be a combination of these prime factors.

for example, 2 * 36 is equal to 2 * (2 * 2 * 3 * 3) which is equal to 2 * 36.

now, if you allow the length of each ribbon to include fractions of an integer, then there are an infininate number of possibilities.

no matter how small you wish to slice each piece, you will always be able to slice each piece even smaller by just cutting the size of each piece in half over and over and over again.

there will reach a point where your scissors just won't be up to the task, but in theory, you can cut them smaller and smaller forever.

consequently, i assumed you wanted each piece to be an integer.

this is what i showed you above.

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