What is the Greatest Common Factor of 22314 and 22320?

Greatest common factor (GCF) of 22314 and 22320 is 6.

GCF(22314,22320) = 6

We will now calculate the prime factors of 22314 and 22320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22314 and 22320.

How to find the GCF of 22314 and 22320?

We will first find the prime factorization of 22314 and 22320. After we will calculate the factors of 22314 and 22320 and find the biggest common factor number .

Step-1: Prime Factorization of 22314

Prime factors of 22314 are 2, 3, 3719. Prime factorization of 22314 in exponential form is:

22314 = 2¹ × 3¹ × 3719¹

Step-2: Prime Factorization of 22320

Prime factors of 22320 are 2, 3, 5, 31. Prime factorization of 22320 in exponential form is:

22320 = 2⁴ × 3² × 5¹ × 31¹

Step-3: Factors of 22314

List of positive integer factors of 22314 that divides 22314 without a remainder.

1, 2, 3, 6, 3719, 7438, 11157

Step-4: Factors of 22320

List of positive integer factors of 22320 that divides 22314 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 31, 36, 40, 45, 48, 60, 62, 72, 80, 90, 93, 120, 124, 144, 155, 180, 186, 240, 248, 279, 310, 360, 372, 465, 496, 558, 620, 720, 744, 930, 1116, 1240, 1395, 1488, 1860, 2232, 2480, 2790, 3720, 4464, 5580, 7440, 11160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22314 and 22320. The biggest common factor number is the GCF number.
So the greatest common factor 22314 and 22320 is 6.

Also check out the Least Common Multiple of 22314 and 22320