Factoring and Multiples

What is the greatest common factor of 289 and 589?



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1 One way to determine the greatest common factor is to find all the factors of the numbers and compare them.

The factors of 289 are 1, 17, and 289.

The factors of 589 are 1, 19, 31, and 589.

The common factors are 1. Therefore, the greatest common factor is 1; they are relatively prime.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.

The prime factors of 289 are 17 and 17.

The prime factors of 589 are 19 and 31.

There are no prime factors in common, which means they are relatively prime, so the greatest common factor is 1.