What is the Greatest Common Factor of 31400 and 31420?

Greatest common factor (GCF) of 31400 and 31420 is 20.

GCF(31400,31420) = 20

We will now calculate the prime factors of 31400 and 31420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31400 and 31420.

How to find the GCF of 31400 and 31420?

We will first find the prime factorization of 31400 and 31420. After we will calculate the factors of 31400 and 31420 and find the biggest common factor number .

Step-1: Prime Factorization of 31400

Prime factors of 31400 are 2, 5, 157. Prime factorization of 31400 in exponential form is:

31400 = 2³ × 5² × 157¹

Step-2: Prime Factorization of 31420

Prime factors of 31420 are 2, 5, 1571. Prime factorization of 31420 in exponential form is:

31420 = 2² × 5¹ × 1571¹

Step-3: Factors of 31400

List of positive integer factors of 31400 that divides 31400 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 157, 200, 314, 628, 785, 1256, 1570, 3140, 3925, 6280, 7850, 15700

Step-4: Factors of 31420

List of positive integer factors of 31420 that divides 31400 without a remainder.

1, 2, 4, 5, 10, 20, 1571, 3142, 6284, 7855, 15710

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31400 and 31420. The biggest common factor number is the GCF number.
So the greatest common factor 31400 and 31420 is 20.

Also check out the Least Common Multiple of 31400 and 31420