What is the Greatest Common Factor of 31296 and 31308?

Greatest common factor (GCF) of 31296 and 31308 is 12.

GCF(31296,31308) = 12

We will now calculate the prime factors of 31296 and 31308, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31296 and 31308.

How to find the GCF of 31296 and 31308?

We will first find the prime factorization of 31296 and 31308. After we will calculate the factors of 31296 and 31308 and find the biggest common factor number .

Step-1: Prime Factorization of 31296

Prime factors of 31296 are 2, 3, 163. Prime factorization of 31296 in exponential form is:

31296 = 2⁶ × 3¹ × 163¹

Step-2: Prime Factorization of 31308

Prime factors of 31308 are 2, 3, 2609. Prime factorization of 31308 in exponential form is:

31308 = 2² × 3¹ × 2609¹

Step-3: Factors of 31296

List of positive integer factors of 31296 that divides 31296 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 163, 192, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 5216, 7824, 10432, 15648

Step-4: Factors of 31308

List of positive integer factors of 31308 that divides 31296 without a remainder.

1, 2, 3, 4, 6, 12, 2609, 5218, 7827, 10436, 15654

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31296 and 31308. The biggest common factor number is the GCF number.
So the greatest common factor 31296 and 31308 is 12.

Also check out the Least Common Multiple of 31296 and 31308