Brennan has 32 forks and 40 knives to place in cutlery holders at the fast food restaurant where he works. He wants to distribute them equally, with no forks or knives left over. What is the greatest number of cutlery holders Brennan can stock?
Question
Brennan has 32 forks and 40 knives to place in cutlery holders at the fast food restaurant where he works. He wants to distribute them equally, with no forks or knives left over. What is the greatest number of cutlery holders Brennan can stock?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of forks (32) and knives (40). 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:
32 = 2 x 2 x 2 x 2 x 2 40 = 2 x 2 x 2 x 5
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Identify the common prime factors:
The common prime factors are 2, 2, and 2.
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Multiply the common prime factors:
2 x 2 x 2 = 8
So, the greatest number of cutlery holders Brennan can stock is 8.
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