What is the Greatest Common Factor of 22305 and 22320?

Greatest common factor (GCF) of 22305 and 22320 is 15.

GCF(22305,22320) = 15

We will now calculate the prime factors of 22305 and 22320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22305 and 22320.

How to find the GCF of 22305 and 22320?

We will first find the prime factorization of 22305 and 22320. After we will calculate the factors of 22305 and 22320 and find the biggest common factor number .

Step-1: Prime Factorization of 22305

Prime factors of 22305 are 3, 5, 1487. Prime factorization of 22305 in exponential form is:

22305 = 3¹ × 5¹ × 1487¹

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 22305

List of positive integer factors of 22305 that divides 22305 without a remainder.

1, 3, 5, 15, 1487, 4461, 7435

Step-4: Factors of 22320

List of positive integer factors of 22320 that divides 22305 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 22305 and 22320. The biggest common factor number is the GCF number.
So the greatest common factor 22305 and 22320 is 15.

Also check out the Least Common Multiple of 22305 and 22320