What is the greatest common factor of 28 and 45?

Answer 1

One is the only factor that is common to both of those numbers.

Factors of 28: 1 2 4 7 14 28

Factors of 45: 1 3 5 9 15 45

The GCF of 28 and 45 is 1

Another way to approach this is to look at the difference between 28 and 45, which is 17. The greatest common factor of two numbers cannot be larger than the difference between the two numbers. The greatest common factor of two numbers must also be a factor of the difference between the numbers. The difference, 17, is a Prime number, so the greatest common factor must be either 17 or 1. Since the numbers are not evenly divisible by 17, the greatest common factor is 1.