Matthew is creating lollipop bouquets using 15 cherry lollipops and 33 orange lollipops. He wants each bouquet to be identical, with no lollipops left over. What is the greatest number of lollipop bouquets Matthew can create?
Question
Matthew is creating lollipop bouquets using 15 cherry lollipops and 33 orange lollipops. He wants each bouquet to be identical, with no lollipops left over. What is the greatest number of lollipop bouquets Matthew can create?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of cherry lollipops (15) and the number of orange lollipops (33). The GCD is the largest number that divides both numbers without leaving a remainder.
Here are the steps to find the GCD of 15 and 33:
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List the prime factors of each number:
- The prime factors of 15 are 3 and 5.
- The prime factors of 33 are 3 and 11.
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Identify the common prime factors:
- The only common prime factor between 15 and 33 is 3.
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The GCD is the product of all the common prime factors:
- In this case, the GCD is 3.
Therefore, the greatest number of identical lollipop bouquets Matthew can create is 3.
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