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The greatest common factor of the set of numbers from 1 to 20 is 1

Definition: A factor is a divisor - a number that will evenly divide into another number. The greatest common factor of two or more numbers is the largest factor that all the numbers have in common.

Methods:

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

The factor of 1 is 1.

The factors of 2 are 1 and 2.

The factors of 3 are 1 and 3.

The factors of 4 are 1, 2, and 4.

The factors of 5 are 1 and 5.

The factors of 6 are 1, 2, 3, and 6.

The factors of 7 are 1 and 7.

The factors of 8 are 1, 2, 4, and 8.

The factors of 9 are 1, 3, and 9.

The factors of 10 are 1, 2, 5, and 10.

The factors of 11 are 1 and 11.

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The factors of 13 are 1 and 13.

The factors of 14 are 1, 2, 7, and 14.

The factors of 15 are 1, 3, 5, and 15.

The factors of 16 are 1, 2, 4, 8, and 16.

The factors of 17 are 1 and 17.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The factors of 19 are 1 and 19.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

The only common factor is 1. Therefore, the greatest common factor is 1, which means the numbers are relatively prime.

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

The only factor of 1 is 1.

The prime factor of 2 is 2.

The prime factor of 3 is 3.

The prime factors of 4 are 2 and 2.

The prime factor of 5 is 5.

The prime factors of 6 are 2 and 3.

The prime factor of 7 is 7.

The prime factors of 8 are 2, 2, and 2.

The prime factors of 9 are 3 and 3.

The prime factors of 10 are 2 and 5.

The prime factor of 11 is 11.

The prime factors of 12 are 2, 2, and 3.

The prime factor of 13 is 13.

The prime factors of 14 are 2 and 7.

The prime factors of 15 are 3 and 5.

The prime factors of 16 are 2, 2, 2, and 2.

The prime factor of 17 is 17.

The prime factors of 18 are 2, 3, and 3.

The prime factor of 19 is 19.

The prime factors of 20 are 2, 2, and 5.

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

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Q: What is the greatest common factor of the numbers 1 through 20?
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