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.