What is the Greatest Common Factor of 52299 and 52314?

Greatest common factor (GCF) of 52299 and 52314 is 3.

GCF(52299,52314) = 3

We will now calculate the prime factors of 52299 and 52314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52299 and 52314.

How to find the GCF of 52299 and 52314?

We will first find the prime factorization of 52299 and 52314. After we will calculate the factors of 52299 and 52314 and find the biggest common factor number .

Step-1: Prime Factorization of 52299

Prime factors of 52299 are 3, 13, 149. Prime factorization of 52299 in exponential form is:

52299 = 3³ × 13¹ × 149¹

Step-2: Prime Factorization of 52314

Prime factors of 52314 are 2, 3, 8719. Prime factorization of 52314 in exponential form is:

52314 = 2¹ × 3¹ × 8719¹

Step-3: Factors of 52299

List of positive integer factors of 52299 that divides 52299 without a remainder.

1, 3, 9, 13, 27, 39, 117, 149, 351, 447, 1341, 1937, 4023, 5811, 17433

Step-4: Factors of 52314

List of positive integer factors of 52314 that divides 52299 without a remainder.

1, 2, 3, 6, 8719, 17438, 26157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52299 and 52314. The biggest common factor number is the GCF number.
So the greatest common factor 52299 and 52314 is 3.

Also check out the Least Common Multiple of 52299 and 52314