Question

A choir teacher is dividing 12 sopranos and 9 altos into singing groups. He wants each group to have the same combination of sopranos and altos, with no singers left over. What is the greatest number of groups he can make?

Answer 1

3 groups

Explanation:

Sopranos = 12

Altos = 9

Find the highest common factor of 12 and 9

12 = 1, 2, 3, 4, 6, 12

9 = 1, 3, 9

The highest common factor of 12 and 9 is 3

Therefore, the choir teacher can only have 3 groups

12 sopranos / 3 groups

= 4 sopranos per group

9 Altos / 3 groups

= 3 altos per group

Each of the 3 groups Will have 4 sopranos and 3 altos each