Answer :
Final answer:
The greatest length for each piece of ribbon that Nisha can cut from her 28 inches red ribbon and 36 inches green ribbon, such that both have equal lengths, is 4 inches.
Explanation:
In this problem, we need to find the greatest length for each piece of ribbon that can be cut from both 28 inches of red ribbon and 36 inches of green ribbon, such that both have equal lengths. This is essentially a problem of determining the greatest common divisor (GCD), also known as the greatest common factor (GCF), of the two lengths 28 and 36. In mathematics, the GCD of two numbers is the largest positive integer that divides both numbers without leaving a remainder.
Divide 28 and 36 by the numbers 1 to 28 (since 28 is the smaller number), to find the greatest common factor. Doing this, we find that the numbers that divide both 28 and 36 are 1, 2, 4, and 7. Out of these, the greatest number is 4. Therefore, the greatest length that both pieces of ribbon can be cut into is 4 inches.
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