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A club has $10$ girls and $15$ 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? $\newline$ $\_\_\_\_$ groups

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GCF and LCM: word problems

Full solution

Q. A club has

10

girls and

15

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?

\newline

\_\_\_\_

groups

Find GCF: First, we need to find the greatest number of groups that can be formed without leaving anyone out. This means finding the greatest common factor (GCF) of the number of girls and boys.
Factors and GCF: Number of girls: $10$ , Number of boys: $15$ . Let's list the factors of each: $\newline$ Factors of $10$ : $1$ , $2$ , $5$ , $10$ $\newline$ Factors of $15$ : $1$ , $3$ , $5$ , $15$ $\newline$ The common factors are $1$ and $5$ , so the GCF is $5$ .
Number of Groups: Therefore, the greatest number of groups that can be formed is $5$ . Each group will have $2$ girls and $3$ boys.

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