IXL | GCF and LCM: word problems

A P.E. teacher needs to divide 15 male students and 9 female students into teams, each with the same combination of male students and female students and nobody left out. What is the greatest number of teams that can be formed?

teams

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Learn with an example

question

Amy wants to display 8 photos and 16 drawings she owns in groups, with each group having the same combination of photos and drawings and none left over. What is the greatest number of groups Amy can display?

groups

key idea

The greatest common factor is the largest whole number that is a factor of each of two or more numbers.

solution

Write the prime factorization for each number.

8	=	2 × 2 × 2

16	=	2 × 2 × 2 × 2

Next, find the common factors shared by both of the numbers.

8	=	2 × 2 × 2

16	=	2 × 2 × 2 × 2

Finally, multiply the common factors to find the greatest common factor.

2 × 2 × 2 = 8

The greatest common factor of 8 and 16 is 8. That means that the greatest possible number of groups is 8, because 8 photos could be split into 8 groups of 1 photo and 16 drawings could be split into 8 groups of 2 drawings.

The greatest number of groups Amy can display is 8.

Looking for more? Try these:

Lesson: Greatest common factor

Lesson: Least common multiple

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Lesson: Greatest common factor

Lesson: Least common multiple

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