What is the Greatest Common Factor of 21312 and 21322?

Greatest common factor (GCF) of 21312 and 21322 is 2.

GCF(21312,21322) = 2

We will now calculate the prime factors of 21312 and 21322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21312 and 21322.

How to find the GCF of 21312 and 21322?

We will first find the prime factorization of 21312 and 21322. After we will calculate the factors of 21312 and 21322 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21322

Prime factors of 21322 are 2, 7, 1523. Prime factorization of 21322 in exponential form is:

21322 = 2¹ × 7¹ × 1523¹

Step-3: Factors of 21312

List of positive integer factors of 21312 that divides 21312 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

Step-4: Factors of 21322

List of positive integer factors of 21322 that divides 21312 without a remainder.

1, 2, 7, 14, 1523, 3046, 10661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21312 and 21322. The biggest common factor number is the GCF number.
So the greatest common factor 21312 and 21322 is 2.

Also check out the Least Common Multiple of 21312 and 21322