What is the Greatest Common Factor of 21675 and 21692?

Greatest common factor (GCF) of 21675 and 21692 is 17.

GCF(21675,21692) = 17

We will now calculate the prime factors of 21675 and 21692, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21675 and 21692.

How to find the GCF of 21675 and 21692?

We will first find the prime factorization of 21675 and 21692. After we will calculate the factors of 21675 and 21692 and find the biggest common factor number .

Step-1: Prime Factorization of 21675

Prime factors of 21675 are 3, 5, 17. Prime factorization of 21675 in exponential form is:

21675 = 3¹ × 5² × 17²

Step-2: Prime Factorization of 21692

Prime factors of 21692 are 2, 11, 17, 29. Prime factorization of 21692 in exponential form is:

21692 = 2² × 11¹ × 17¹ × 29¹

Step-3: Factors of 21675

List of positive integer factors of 21675 that divides 21675 without a remainder.

1, 3, 5, 15, 17, 25, 51, 75, 85, 255, 289, 425, 867, 1275, 1445, 4335, 7225

Step-4: Factors of 21692

List of positive integer factors of 21692 that divides 21675 without a remainder.

1, 2, 4, 11, 17, 22, 29, 34, 44, 58, 68, 116, 187, 319, 374, 493, 638, 748, 986, 1276, 1972, 5423, 10846

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21675 and 21692. The biggest common factor number is the GCF number.
So the greatest common factor 21675 and 21692 is 17.

Also check out the Least Common Multiple of 21675 and 21692