What is the Greatest Common Factor of 31297 and 31314?

Greatest common factor (GCF) of 31297 and 31314 is 17.

GCF(31297,31314) = 17

We will now calculate the prime factors of 31297 and 31314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31297 and 31314.

How to find the GCF of 31297 and 31314?

We will first find the prime factorization of 31297 and 31314. After we will calculate the factors of 31297 and 31314 and find the biggest common factor number .

Step-1: Prime Factorization of 31297

Prime factors of 31297 are 7, 17, 263. Prime factorization of 31297 in exponential form is:

31297 = 7¹ × 17¹ × 263¹

Step-2: Prime Factorization of 31314

Prime factors of 31314 are 2, 3, 17, 307. Prime factorization of 31314 in exponential form is:

31314 = 2¹ × 3¹ × 17¹ × 307¹

Step-3: Factors of 31297

List of positive integer factors of 31297 that divides 31297 without a remainder.

1, 7, 17, 119, 263, 1841, 4471

Step-4: Factors of 31314

List of positive integer factors of 31314 that divides 31297 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31297 and 31314. The biggest common factor number is the GCF number.
So the greatest common factor 31297 and 31314 is 17.

Also check out the Least Common Multiple of 31297 and 31314