Megan is creating party favors with pencils and stickers. She has 18 pencils and 45 stickers, and wants each party favor to include the same combination of pencils and stickers, with none left over. What is the greatest number of party favors she can make?
Question
Megan is creating party favors with pencils and stickers. She has 18 pencils and 45 stickers, and wants each party favor to include the same combination of pencils and stickers, with none left over. What is the greatest number of party favors she can make?
Solution
To find the greatest number of party favors Megan can make, we need to determine the common combination of pencils and stickers that can be evenly distributed among them.
First, let's find the greatest common divisor (GCD) of 18 and 45. The GCD represents the largest number that divides both 18 and 45 without leaving a remainder.
The prime factorization of 18 is 2 * 3^2, and the prime factorization of 45 is 3^2 * 5.
To find the GCD, we take the highest power of each common prime factor. In this case, the highest power of 3 is 3^2, so the GCD is 3^2 = 9.
Therefore, Megan can make the greatest number of party favors by using 9 pencils and 9 stickers in each favor.
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