What is the Greatest Common Factor of 31698 and 31714?

Greatest common factor (GCF) of 31698 and 31714 is 2.

GCF(31698,31714) = 2

We will now calculate the prime factors of 31698 and 31714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31698 and 31714.

How to find the GCF of 31698 and 31714?

We will first find the prime factorization of 31698 and 31714. After we will calculate the factors of 31698 and 31714 and find the biggest common factor number .

Step-1: Prime Factorization of 31698

Prime factors of 31698 are 2, 3, 587. Prime factorization of 31698 in exponential form is:

31698 = 2¹ × 3³ × 587¹

Step-2: Prime Factorization of 31714

Prime factors of 31714 are 2, 101, 157. Prime factorization of 31714 in exponential form is:

31714 = 2¹ × 101¹ × 157¹

Step-3: Factors of 31698

List of positive integer factors of 31698 that divides 31698 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 587, 1174, 1761, 3522, 5283, 10566, 15849

Step-4: Factors of 31714

List of positive integer factors of 31714 that divides 31698 without a remainder.

1, 2, 101, 157, 202, 314, 15857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31698 and 31714. The biggest common factor number is the GCF number.
So the greatest common factor 31698 and 31714 is 2.

Also check out the Least Common Multiple of 31698 and 31714