What is the Greatest Common Factor of 23205 and 23214?

Greatest common factor (GCF) of 23205 and 23214 is 3.

GCF(23205,23214) = 3

We will now calculate the prime factors of 23205 and 23214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23205 and 23214.

How to find the GCF of 23205 and 23214?

We will first find the prime factorization of 23205 and 23214. After we will calculate the factors of 23205 and 23214 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 23214

Prime factors of 23214 are 2, 3, 53, 73. Prime factorization of 23214 in exponential form is:

23214 = 2¹ × 3¹ × 53¹ × 73¹

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 23214

List of positive integer factors of 23214 that divides 23205 without a remainder.

1, 2, 3, 6, 53, 73, 106, 146, 159, 219, 318, 438, 3869, 7738, 11607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23205 and 23214. The biggest common factor number is the GCF number.
So the greatest common factor 23205 and 23214 is 3.

Also check out the Least Common Multiple of 23205 and 23214