What is the Greatest Common Factor of 21300 and 21312?

Greatest common factor (GCF) of 21300 and 21312 is 12.

GCF(21300,21312) = 12

We will now calculate the prime factors of 21300 and 21312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21300 and 21312.

How to find the GCF of 21300 and 21312?

We will first find the prime factorization of 21300 and 21312. After we will calculate the factors of 21300 and 21312 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21312

Prime factors of 21312 are 2, 3, 37. Prime factorization of 21312 in exponential form is:

21312 = 2⁶ × 3² × 37¹

Step-3: Factors of 21300

List of positive integer factors of 21300 that divides 21300 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

Step-4: Factors of 21312

List of positive integer factors of 21312 that divides 21300 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 37, 48, 64, 72, 74, 96, 111, 144, 148, 192, 222, 288, 296, 333, 444, 576, 592, 666, 888, 1184, 1332, 1776, 2368, 2664, 3552, 5328, 7104, 10656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21300 and 21312. The biggest common factor number is the GCF number.
So the greatest common factor 21300 and 21312 is 12.

Also check out the Least Common Multiple of 21300 and 21312