What is the Greatest Common Factor of 31698 and 31708?

Greatest common factor (GCF) of 31698 and 31708 is 2.

GCF(31698,31708) = 2

We will now calculate the prime factors of 31698 and 31708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31698 and 31708.

How to find the GCF of 31698 and 31708?

We will first find the prime factorization of 31698 and 31708. After we will calculate the factors of 31698 and 31708 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 31708

Prime factors of 31708 are 2, 7927. Prime factorization of 31708 in exponential form is:

31708 = 2² × 7927¹

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 31708

List of positive integer factors of 31708 that divides 31698 without a remainder.

1, 2, 4, 7927, 15854

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31698 and 31708. The biggest common factor number is the GCF number.
So the greatest common factor 31698 and 31708 is 2.

Also check out the Least Common Multiple of 31698 and 31708