What is the Greatest Common Factor of 21357 and 21364?

Greatest common factor (GCF) of 21357 and 21364 is 7.

GCF(21357,21364) = 7

We will now calculate the prime factors of 21357 and 21364, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21357 and 21364.

How to find the GCF of 21357 and 21364?

We will first find the prime factorization of 21357 and 21364. After we will calculate the factors of 21357 and 21364 and find the biggest common factor number .

Step-1: Prime Factorization of 21357

Prime factors of 21357 are 3, 7, 113. Prime factorization of 21357 in exponential form is:

21357 = 3³ × 7¹ × 113¹

Step-2: Prime Factorization of 21364

Prime factors of 21364 are 2, 7, 109. Prime factorization of 21364 in exponential form is:

21364 = 2² × 7² × 109¹

Step-3: Factors of 21357

List of positive integer factors of 21357 that divides 21357 without a remainder.

1, 3, 7, 9, 21, 27, 63, 113, 189, 339, 791, 1017, 2373, 3051, 7119

Step-4: Factors of 21364

List of positive integer factors of 21364 that divides 21357 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 109, 196, 218, 436, 763, 1526, 3052, 5341, 10682

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21357 and 21364. The biggest common factor number is the GCF number.
So the greatest common factor 21357 and 21364 is 7.

Also check out the Least Common Multiple of 21357 and 21364