What is the Greatest Common Factor of 21664 and 21675?

Greatest common factor (GCF) of 21664 and 21675 is 1.

GCF(21664,21675) = 1

We will now calculate the prime factors of 21664 and 21675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21664 and 21675.

How to find the GCF of 21664 and 21675?

We will first find the prime factorization of 21664 and 21675. After we will calculate the factors of 21664 and 21675 and find the biggest common factor number .

Step-1: Prime Factorization of 21664

Prime factors of 21664 are 2, 677. Prime factorization of 21664 in exponential form is:

21664 = 2⁵ × 677¹

Step-2: 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-3: Factors of 21664

List of positive integer factors of 21664 that divides 21664 without a remainder.

1, 2, 4, 8, 16, 32, 677, 1354, 2708, 5416, 10832

Step-4: Factors of 21675

List of positive integer factors of 21675 that divides 21664 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21664 and 21675. The biggest common factor number is the GCF number.
So the greatest common factor 21664 and 21675 is 1.

Also check out the Least Common Multiple of 21664 and 21675