What is the Greatest Common Factor of 31400 and 31416?

Greatest common factor (GCF) of 31400 and 31416 is 8.

GCF(31400,31416) = 8

We will now calculate the prime factors of 31400 and 31416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31400 and 31416.

How to find the GCF of 31400 and 31416?

We will first find the prime factorization of 31400 and 31416. After we will calculate the factors of 31400 and 31416 and find the biggest common factor number .

Step-1: Prime Factorization of 31400

Prime factors of 31400 are 2, 5, 157. Prime factorization of 31400 in exponential form is:

31400 = 2³ × 5² × 157¹

Step-2: Prime Factorization of 31416

Prime factors of 31416 are 2, 3, 7, 11, 17. Prime factorization of 31416 in exponential form is:

31416 = 2³ × 3¹ × 7¹ × 11¹ × 17¹

Step-3: Factors of 31400

List of positive integer factors of 31400 that divides 31400 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 157, 200, 314, 628, 785, 1256, 1570, 3140, 3925, 6280, 7850, 15700

Step-4: Factors of 31416

List of positive integer factors of 31416 that divides 31400 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 17, 21, 22, 24, 28, 33, 34, 42, 44, 51, 56, 66, 68, 77, 84, 88, 102, 119, 132, 136, 154, 168, 187, 204, 231, 238, 264, 308, 357, 374, 408, 462, 476, 561, 616, 714, 748, 924, 952, 1122, 1309, 1428, 1496, 1848, 2244, 2618, 2856, 3927, 4488, 5236, 7854, 10472, 15708

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31400 and 31416. The biggest common factor number is the GCF number.
So the greatest common factor 31400 and 31416 is 8.

Also check out the Least Common Multiple of 31400 and 31416