What is the Greatest Common Factor of 31296 and 31302?

Greatest common factor (GCF) of 31296 and 31302 is 6.

GCF(31296,31302) = 6

We will now calculate the prime factors of 31296 and 31302, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31296 and 31302.

How to find the GCF of 31296 and 31302?

We will first find the prime factorization of 31296 and 31302. After we will calculate the factors of 31296 and 31302 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 31302

Prime factors of 31302 are 2, 3, 37, 47. Prime factorization of 31302 in exponential form is:

31302 = 2¹ × 3² × 37¹ × 47¹

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 31302

List of positive integer factors of 31302 that divides 31296 without a remainder.

1, 2, 3, 6, 9, 18, 37, 47, 74, 94, 111, 141, 222, 282, 333, 423, 666, 846, 1739, 3478, 5217, 10434, 15651

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31296 and 31302. The biggest common factor number is the GCF number.
So the greatest common factor 31296 and 31302 is 6.

Also check out the Least Common Multiple of 31296 and 31302