What is the Greatest Common Factor of 23205 and 23220?

Greatest common factor (GCF) of 23205 and 23220 is 15.

GCF(23205,23220) = 15

We will now calculate the prime factors of 23205 and 23220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23205 and 23220.

How to find the GCF of 23205 and 23220?

We will first find the prime factorization of 23205 and 23220. After we will calculate the factors of 23205 and 23220 and find the biggest common factor number .

Step-1: Prime Factorization of 23205

Prime factors of 23205 are 3, 5, 7, 13, 17. Prime factorization of 23205 in exponential form is:

23205 = 3¹ × 5¹ × 7¹ × 13¹ × 17¹

Step-2: Prime Factorization of 23220

Prime factors of 23220 are 2, 3, 5, 43. Prime factorization of 23220 in exponential form is:

23220 = 2² × 3³ × 5¹ × 43¹

Step-3: Factors of 23205

List of positive integer factors of 23205 that divides 23205 without a remainder.

1, 3, 5, 7, 13, 15, 17, 21, 35, 39, 51, 65, 85, 91, 105, 119, 195, 221, 255, 273, 357, 455, 595, 663, 1105, 1365, 1547, 1785, 3315, 4641, 7735

Step-4: Factors of 23220

List of positive integer factors of 23220 that divides 23205 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 43, 45, 54, 60, 86, 90, 108, 129, 135, 172, 180, 215, 258, 270, 387, 430, 516, 540, 645, 774, 860, 1161, 1290, 1548, 1935, 2322, 2580, 3870, 4644, 5805, 7740, 11610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23205 and 23220. The biggest common factor number is the GCF number.
So the greatest common factor 23205 and 23220 is 15.

Also check out the Least Common Multiple of 23205 and 23220