What is the Greatest Common Factor of 21296 and 21300?

Greatest common factor (GCF) of 21296 and 21300 is 4.

GCF(21296,21300) = 4

We will now calculate the prime factors of 21296 and 21300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21296 and 21300.

How to find the GCF of 21296 and 21300?

We will first find the prime factorization of 21296 and 21300. After we will calculate the factors of 21296 and 21300 and find the biggest common factor number .

Step-1: Prime Factorization of 21296

Prime factors of 21296 are 2, 11. Prime factorization of 21296 in exponential form is:

21296 = 2⁴ × 11³

Step-2: Prime Factorization of 21300

Prime factors of 21300 are 2, 3, 5, 71. Prime factorization of 21300 in exponential form is:

21300 = 2² × 3¹ × 5² × 71¹

Step-3: Factors of 21296

List of positive integer factors of 21296 that divides 21296 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 121, 176, 242, 484, 968, 1331, 1936, 2662, 5324, 10648

Step-4: Factors of 21300

List of positive integer factors of 21300 that divides 21296 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 71, 75, 100, 142, 150, 213, 284, 300, 355, 426, 710, 852, 1065, 1420, 1775, 2130, 3550, 4260, 5325, 7100, 10650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21296 and 21300. The biggest common factor number is the GCF number.
So the greatest common factor 21296 and 21300 is 4.

Also check out the Least Common Multiple of 21296 and 21300