A P.E. teacher needs to divide 20 male students and 16 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?
Question
A P.E. teacher needs to divide 20 male students and 16 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?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of male students (20) and the number of female students (16). The GCD is the largest number that can divide both numbers without leaving a remainder.
Here are the steps to find the GCD:
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List the prime factors of each number:
- The prime factors of 20 are 2, 2, 5.
- The prime factors of 16 are 2, 2, 2, 2.
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Identify the common prime factors:
- The common prime factors are 2, 2.
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Multiply the common prime factors to get the GCD:
- The GCD is 2 * 2 = 4.
So, the greatest number of teams that can be formed, each with the same combination of male students and female students and nobody left out, is 4.
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