Gina wants to sell 49 chocolate chip cookies and 35 sugar cookies. She is going to sell them on plates with equal amounts on each plate. Each plate needs to hold the largest number of cookies, without mixing types of cookies. How many cookies should Gina put on each plate?
Question
Gina wants to sell 49 chocolate chip cookies and 35 sugar cookies. She is going to sell them on plates with equal amounts on each plate. Each plate needs to hold the largest number of cookies, without mixing types of cookies. How many cookies should Gina put on each plate?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the two numbers, 49 and 35. The GCD is the largest number that divides both numbers without leaving a remainder.
Here are the steps:
-
List the prime factors of each number:
- The prime factors of 49 are 7 and 7.
- The prime factors of 35 are 5 and 7.
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Identify the common prime factors:
- The common prime factor is 7.
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Multiply the common prime factors:
- 7
So, Gina should put 7 cookies on each plate.
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