There are 48 boys and 60 girls that need to be split up into even teams for a PE activity. What is the greatest number of teams that can be formed if the same number of boys and girls need to be on each team? How many boys and girls will be on each team?

Expert Answers

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If we could split boys and girls into n teams, and b boys and g girls will be in each team, then obviously `nb=48` and `ng=60.` Therefore `n` divides 48 and `n` divides 60, or the same may be formulated as "`n` is a common divisor of 48 and 60". And the greatest such number is the greatest common divisor (GCD) of 48 and 60.

One way to find it is to factor 48 and 60 into prime factors:

`48=6*8=3*2^4,`
`60=6*10=5*3*2^2.`

There are common prime divisors `3` and `2^2,` GCD is their product which is  `12.`

So the answer is: 12 commands is the maximum. Each of them will consist of 48/12=4 boys and 60/12=5 girls.

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