Question: A choir teacher is dividing 15 sopranos and 6 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?
(1) 2
(2) 3
(3) 5
(4) 2.5
Solution
Write the prime factorisation for each number.
15 = 3 × 5
6 = 2 × 3
Next, find the common factors shared by both of the numbers.
15 = 3 × 5
6 = 2 × 3
The only common factor of 15 and 6 is 3, so the highest common factor is 3. That means that the greatest possible number of groups is 3, because 15 sopranos could be split into 3 groups with 5 sopranos each and 6 altos could be split into 3 groups with 2 altos each.
The greatest number of groups he can make is 3.
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