Question

Lincoln has collected 27 jeans and 45 shirts from his favorite band. He wants to combine them into identical sets to sell, with no pieces left over. What is the greatest number of sets Lincoln can make?

• A. 3
• B. 9
• C. 15

Answer 1

The correct option is B 9

List the factors of each number. Find the largest number that appears in both lists.

Factors of 27: 1, 3, 9 and 27
Factors of 45: 1, 3, 5, 9, 15 and 45

The greatest common factor of 27 and 45 is 9. That means that the greatest possible number of sets is 9.

Each set could contain 3 jeans as 3 × 9 = 27 (27 jeans)
Each set could contain 5 shirts as 5 × 9 = 45 (45 jeans)

Thus, the greatest number of sets Lincoln can make is 9.