What is the Greatest Common Factor of 31900 and 31909?

Greatest common factor (GCF) of 31900 and 31909 is 1.

GCF(31900,31909) = 1

We will now calculate the prime factors of 31900 and 31909, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31900 and 31909.

How to find the GCF of 31900 and 31909?

We will first find the prime factorization of 31900 and 31909. After we will calculate the factors of 31900 and 31909 and find the biggest common factor number .

Step-1: Prime Factorization of 31900

Prime factors of 31900 are 2, 5, 11, 29. Prime factorization of 31900 in exponential form is:

31900 = 2² × 5² × 11¹ × 29¹

Step-2: Prime Factorization of 31909

Prime factors of 31909 are 17, 1877. Prime factorization of 31909 in exponential form is:

31909 = 17¹ × 1877¹

Step-3: Factors of 31900

List of positive integer factors of 31900 that divides 31900 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 29, 44, 50, 55, 58, 100, 110, 116, 145, 220, 275, 290, 319, 550, 580, 638, 725, 1100, 1276, 1450, 1595, 2900, 3190, 6380, 7975, 15950

Step-4: Factors of 31909

List of positive integer factors of 31909 that divides 31900 without a remainder.

1, 17, 1877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31900 and 31909. The biggest common factor number is the GCF number.
So the greatest common factor 31900 and 31909 is 1.

Also check out the Least Common Multiple of 31900 and 31909