What is the Greatest Common Factor of 31314 and 31331?

Greatest common factor (GCF) of 31314 and 31331 is 17.

GCF(31314,31331) = 17

We will now calculate the prime factors of 31314 and 31331, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31314 and 31331.

How to find the GCF of 31314 and 31331?

We will first find the prime factorization of 31314 and 31331. After we will calculate the factors of 31314 and 31331 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31331

Prime factors of 31331 are 17, 19, 97. Prime factorization of 31331 in exponential form is:

31331 = 17¹ × 19¹ × 97¹

Step-3: Factors of 31314

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

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

Step-4: Factors of 31331

List of positive integer factors of 31331 that divides 31314 without a remainder.

1, 17, 19, 97, 323, 1649, 1843

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31314 and 31331. The biggest common factor number is the GCF number.
So the greatest common factor 31314 and 31331 is 17.

Also check out the Least Common Multiple of 31314 and 31331