Makayla has two types of ropes. she wants to cut the ropes into pieces of the same length for butterfly knots. one is 84 inches, the other is 116 inches. find the greatest possible length that she can cut for each piece, so that no rope will be left unused.

Remark

If you want every piece you cut equal to the same length, you are talking about the GCF because both ropes have to be cut in such a way that all parts of the whole set of ropes are the same size.

Prime Factors of 84 and 116

84: 2 * 2 * 3 * 7

116: 2 * 2 * 29

The two 2s are all that is common.

So that means that the 84 inch length will give you 21 lengths that are 4 inches long and the 116 inch length will give you 29 lengths that are 4 inches long.

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