A club has 8 girls and 18 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups the president can make?
Question
A club has 8 girls and 18 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups the president can make?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of girls and boys in the club. The GCD is the largest number that can divide both numbers without leaving a remainder.
Here are the steps:
- List the divisors of 8: 1, 2, 4, 8
- List the divisors of 18: 1, 2, 3, 6, 9, 18
- Find the greatest number that appears in both lists: 2
So, the president can make 2 groups, with each group containing 4 girls and 9 boys.
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