What is the Greatest Common Factor of 72297 and 72312?

Greatest common factor (GCF) of 72297 and 72312 is 3.

GCF(72297,72312) = 3

We will now calculate the prime factors of 72297 and 72312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72297 and 72312.

How to find the GCF of 72297 and 72312?

We will first find the prime factorization of 72297 and 72312. After we will calculate the factors of 72297 and 72312 and find the biggest common factor number .

Step-1: Prime Factorization of 72297

Prime factors of 72297 are 3, 29, 277. Prime factorization of 72297 in exponential form is:

72297 = 3² × 29¹ × 277¹

Step-2: Prime Factorization of 72312

Prime factors of 72312 are 2, 3, 23, 131. Prime factorization of 72312 in exponential form is:

72312 = 2³ × 3¹ × 23¹ × 131¹

Step-3: Factors of 72297

List of positive integer factors of 72297 that divides 72297 without a remainder.

1, 3, 9, 29, 87, 261, 277, 831, 2493, 8033, 24099

Step-4: Factors of 72312

List of positive integer factors of 72312 that divides 72297 without a remainder.

1, 2, 3, 4, 6, 8, 12, 23, 24, 46, 69, 92, 131, 138, 184, 262, 276, 393, 524, 552, 786, 1048, 1572, 3013, 3144, 6026, 9039, 12052, 18078, 24104, 36156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72297 and 72312. The biggest common factor number is the GCF number.
So the greatest common factor 72297 and 72312 is 3.

Also check out the Least Common Multiple of 72297 and 72312