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The GCF of 10 and 21 is 1.
One way to approach this is to look at the difference between 10 and 21, which is 11. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference. The greatest common factor cannot be larger than the smallest number, so it cannot be 11. The only other factor of 11 is 1, so the greatest common factor is 1.
Another way to determine the greatest common factor is to find all the factors of the numbers and compare them.
The factors of 10 are 1, 2, 5, and 10.
The factors of 21 are 1, 3, 7, and 21.
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 prime factors of 10 are 2 and 5.
The prime factors of 21 are 3 and 7.
There are no prime factors in common, so the numbers are relatively prime, which means the greatest common factor is 1.
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