What is the Greatest Common Factor of 21664 and 21677?

Greatest common factor (GCF) of 21664 and 21677 is 1.

GCF(21664,21677) = 1

We will now calculate the prime factors of 21664 and 21677, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21664 and 21677.

How to find the GCF of 21664 and 21677?

We will first find the prime factorization of 21664 and 21677. After we will calculate the factors of 21664 and 21677 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 21677

Prime factors of 21677 are 53, 409. Prime factorization of 21677 in exponential form is:

21677 = 53¹ × 409¹

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 21677

List of positive integer factors of 21677 that divides 21664 without a remainder.

1, 53, 409

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21664 and 21677. The biggest common factor number is the GCF number.
So the greatest common factor 21664 and 21677 is 1.

Also check out the Least Common Multiple of 21664 and 21677