What is the Greatest Common Factor of 22359 and 22365?

Greatest common factor (GCF) of 22359 and 22365 is 3.

GCF(22359,22365) = 3

We will now calculate the prime factors of 22359 and 22365, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22359 and 22365.

How to find the GCF of 22359 and 22365?

We will first find the prime factorization of 22359 and 22365. After we will calculate the factors of 22359 and 22365 and find the biggest common factor number .

Step-1: Prime Factorization of 22359

Prime factors of 22359 are 3, 29, 257. Prime factorization of 22359 in exponential form is:

22359 = 3¹ × 29¹ × 257¹

Step-2: Prime Factorization of 22365

Prime factors of 22365 are 3, 5, 7, 71. Prime factorization of 22365 in exponential form is:

22365 = 3² × 5¹ × 7¹ × 71¹

Step-3: Factors of 22359

List of positive integer factors of 22359 that divides 22359 without a remainder.

1, 3, 29, 87, 257, 771, 7453

Step-4: Factors of 22365

List of positive integer factors of 22365 that divides 22359 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 71, 105, 213, 315, 355, 497, 639, 1065, 1491, 2485, 3195, 4473, 7455

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22359 and 22365. The biggest common factor number is the GCF number.
So the greatest common factor 22359 and 22365 is 3.

Also check out the Least Common Multiple of 22359 and 22365