What is the Greatest Common Factor of 31198 and 31208?

Greatest common factor (GCF) of 31198 and 31208 is 2.

GCF(31198,31208) = 2

We will now calculate the prime factors of 31198 and 31208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31198 and 31208.

How to find the GCF of 31198 and 31208?

We will first find the prime factorization of 31198 and 31208. After we will calculate the factors of 31198 and 31208 and find the biggest common factor number .

Step-1: Prime Factorization of 31198

Prime factors of 31198 are 2, 19, 821. Prime factorization of 31198 in exponential form is:

31198 = 2¹ × 19¹ × 821¹

Step-2: Prime Factorization of 31208

Prime factors of 31208 are 2, 47, 83. Prime factorization of 31208 in exponential form is:

31208 = 2³ × 47¹ × 83¹

Step-3: Factors of 31198

List of positive integer factors of 31198 that divides 31198 without a remainder.

1, 2, 19, 38, 821, 1642, 15599

Step-4: Factors of 31208

List of positive integer factors of 31208 that divides 31198 without a remainder.

1, 2, 4, 8, 47, 83, 94, 166, 188, 332, 376, 664, 3901, 7802, 15604

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31198 and 31208. The biggest common factor number is the GCF number.
So the greatest common factor 31198 and 31208 is 2.

Also check out the Least Common Multiple of 31198 and 31208