What is the Greatest Common Factor of 31400 and 31409?

Greatest common factor (GCF) of 31400 and 31409 is 1.

GCF(31400,31409) = 1

We will now calculate the prime factors of 31400 and 31409, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31400 and 31409.

How to find the GCF of 31400 and 31409?

We will first find the prime factorization of 31400 and 31409. After we will calculate the factors of 31400 and 31409 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 31409

Prime factors of 31409 are 7, 641. Prime factorization of 31409 in exponential form is:

31409 = 7² × 641¹

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 31409

List of positive integer factors of 31409 that divides 31400 without a remainder.

1, 7, 49, 641, 4487

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31400 and 31409. The biggest common factor number is the GCF number.
So the greatest common factor 31400 and 31409 is 1.

Also check out the Least Common Multiple of 31400 and 31409