Quinn is preparing sales kits for her sales representatives to show to customers. She has 64 samples of tile and 86 samples of carpet, and she wants to create identical sales kits, with no samples left over. What is the greatest number of sales kits Quinn can prepare?
Question
Quinn is preparing sales kits for her sales representatives to show to customers. She has 64 samples of tile and 86 samples of carpet, and she wants to create identical sales kits, with no samples left over. What is the greatest number of sales kits Quinn can prepare?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the two numbers, 64 and 86. The GCD is the largest number that divides both numbers without leaving a remainder.
Here are the steps to find the GCD:
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First, list the prime factors of each number.
- The prime factors of 64 are 2 x 2 x 2 x 2 x 2 x 2.
- The prime factors of 86 are 2 x 43.
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Next, identify the common prime factors.
- The common prime factor is 2.
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The GCD is the product of the common prime factors.
- So, the GCD of 64 and 86 is 2.
Therefore, the greatest number of sales kits Quinn can prepare is 2.
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