A family is preparing backpacks filled with school supplies to donate to children in need. They have 12 pencils and 16 notebooks. If they want to make all the backpacks the same, with no school supplies left over, what is the greatest number of backpacks they can fill?
Question
A family is preparing backpacks filled with school supplies to donate to children in need. They have 12 pencils and 16 notebooks. If they want to make all the backpacks the same, with no school supplies left over, what is the greatest number of backpacks they can fill?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of pencils (12) and notebooks (16). The GCD is the largest number that can divide both numbers without leaving a remainder.
Here are the steps to find the GCD:
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List the prime factors of each number:
- The prime factors of 12 are 2, 2, and 3.
- The prime factors of 16 are 2, 2, 2, and 2.
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Identify the common prime factors:
- The common prime factors are 2 and 2.
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Multiply the common prime factors together:
- 2 * 2 = 4
So, the greatest number of backpacks they can fill is 4.
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