High School

Scarlett has 44 meters of blue ribbon and 110 meters of red ribbon. All the ribbon must be cut into smaller pieces with no ribbon left over, and all the pieces must be the same length. What is the longest length she can make each smaller piece of ribbon?

Answer :

To find the longest piece Scarlett can make from both the blue and red ribbons where all pieces are the same length with no ribbon left over, we need to find the greatest common divisor (GCD) of 44 meters (blue ribbon) and 110 meters (red ribbon).

The GCD is the largest number that can evenly divide both numbers without leaving any remainder.

  1. List the factors of each number:

    • Factors of 44: 1, 2, 4, 11, 22, 44
    • Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110

  2. Identify the common factors:
    The common factors of 44 and 110 are 1, 2, 11, and 22.

  3. Find the greatest common factor:
    The greatest common factor is the largest of the common factors, which is 22.

Thus, the longest length for each piece of ribbon that Scarlett can cut, ensuring there is no leftover ribbon, is 22 meters.

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