What is the Greatest Common Factor of 21400 and 21405?

Greatest common factor (GCF) of 21400 and 21405 is 5.

GCF(21400,21405) = 5

We will now calculate the prime factors of 21400 and 21405, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21400 and 21405.

How to find the GCF of 21400 and 21405?

We will first find the prime factorization of 21400 and 21405. After we will calculate the factors of 21400 and 21405 and find the biggest common factor number .

Step-1: Prime Factorization of 21400

Prime factors of 21400 are 2, 5, 107. Prime factorization of 21400 in exponential form is:

21400 = 2³ × 5² × 107¹

Step-2: Prime Factorization of 21405

Prime factors of 21405 are 3, 5, 1427. Prime factorization of 21405 in exponential form is:

21405 = 3¹ × 5¹ × 1427¹

Step-3: Factors of 21400

List of positive integer factors of 21400 that divides 21400 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 107, 200, 214, 428, 535, 856, 1070, 2140, 2675, 4280, 5350, 10700

Step-4: Factors of 21405

List of positive integer factors of 21405 that divides 21400 without a remainder.

1, 3, 5, 15, 1427, 4281, 7135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21400 and 21405. The biggest common factor number is the GCF number.
So the greatest common factor 21400 and 21405 is 5.

Also check out the Least Common Multiple of 21400 and 21405