What is the Greatest Common Factor of 31409 and 31416?

Greatest common factor (GCF) of 31409 and 31416 is 7.

GCF(31409,31416) = 7

We will now calculate the prime factors of 31409 and 31416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31409 and 31416.

How to find the GCF of 31409 and 31416?

We will first find the prime factorization of 31409 and 31416. After we will calculate the factors of 31409 and 31416 and find the biggest common factor number .

Step-1: Prime Factorization of 31409

Prime factors of 31409 are 7, 641. Prime factorization of 31409 in exponential form is:

31409 = 7² × 641¹

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 31409

List of positive integer factors of 31409 that divides 31409 without a remainder.

1, 7, 49, 641, 4487

Step-4: Factors of 31416

List of positive integer factors of 31416 that divides 31409 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 31409 and 31416. The biggest common factor number is the GCF number.
So the greatest common factor 31409 and 31416 is 7.

Also check out the Least Common Multiple of 31409 and 31416