A drama teacher is putting his studentsinto groups. There must be the samenumber of females in each group and thesame number of males in each group.There are 12 males and 18 females. Eachstudent must be in a group. What is thegreatest number of groups there can be?
Question
A drama teacher is putting his studentsinto groups. There must be the samenumber of females in each group and thesame number of males in each group.There are 12 males and 18 females. Eachstudent must be in a group. What is thegreatest number of groups there can be?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of males and females, because the GCD will give us the largest number of groups we can form where each group has the same number of males and females.
Step 1: Find the GCD of 12 (males) and 18 (females).
The factors of 12 are: 1, 2, 3, 4, 6, 12. The factors of 18 are: 1, 2, 3, 6, 9, 18.
The greatest number that is a factor of both 12 and 18 is 6.
Step 2: The GCD of 12 and 18 is 6.
So, the greatest number of groups the drama teacher can form, with an equal number of males and females in each group, is 6.
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