What is the Greatest Common Factor of 21364 and 21380?

Greatest common factor (GCF) of 21364 and 21380 is 4.

GCF(21364,21380) = 4

We will now calculate the prime factors of 21364 and 21380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21364 and 21380.

How to find the GCF of 21364 and 21380?

We will first find the prime factorization of 21364 and 21380. After we will calculate the factors of 21364 and 21380 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21380

Prime factors of 21380 are 2, 5, 1069. Prime factorization of 21380 in exponential form is:

21380 = 2² × 5¹ × 1069¹

Step-3: Factors of 21364

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

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

Step-4: Factors of 21380

List of positive integer factors of 21380 that divides 21364 without a remainder.

1, 2, 4, 5, 10, 20, 1069, 2138, 4276, 5345, 10690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21364 and 21380. The biggest common factor number is the GCF number.
So the greatest common factor 21364 and 21380 is 4.

Also check out the Least Common Multiple of 21364 and 21380