Primes and Composites: There are 20 boys and 24 girls in an Algebra I class. The class is so large that the teacher wants to divide the students into gender-specific groups (all boys or all girls). Each group needs to have the same number of students.

1. Explain the process the teacher will use to determine how many students will be in each group using appropriate mathematical terms from number theory.

They are looking for something like this....

If d is a factor of a, then it is a factor of a multiple of a, call it ra. Similarly, if d is a factor of b, then it is a factor of a multiple of b, call it sb. It must also be a factor of the sum, ra sb because if it is a factor of both ra and sb, then it can be factored out of each term.

the 20 boys and 24 girls of the class are to be parted into groups such that each part comprises only boys or only girls.

for this, if we consider the greatest common divisor of 20 and 24 as the number of students in each group, then the desire of the teacher will be fulfilled.

the factors of 20 are 1, 2, 4, 5, 10, 20

the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

common factors of 20 and 24 are 1, 2, and 4.

greatest common divisor is 4.

therefore, if each group consists of 4 students only, then the entire class can be evenly parted to see that each group consists of only boys or only girls.

Sep 30th, 2014

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