What is the Greatest Common Factor of 31409 and 31413?

Greatest common factor (GCF) of 31409 and 31413 is 1.

GCF(31409,31413) = 1

We will now calculate the prime factors of 31409 and 31413, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31409 and 31413.

How to find the GCF of 31409 and 31413?

We will first find the prime factorization of 31409 and 31413. After we will calculate the factors of 31409 and 31413 and find the biggest common factor number .

Step-1: Prime Factorization of 31409

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

31409 = 7² × 641¹

Step-2: Prime Factorization of 31413

Prime factors of 31413 are 3, 37, 283. Prime factorization of 31413 in exponential form is:

31413 = 3¹ × 37¹ × 283¹

Step-3: Factors of 31409

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

1, 7, 49, 641, 4487

Step-4: Factors of 31413

List of positive integer factors of 31413 that divides 31409 without a remainder.

1, 3, 37, 111, 283, 849, 10471

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31409 and 31413. The biggest common factor number is the GCF number.
So the greatest common factor 31409 and 31413 is 1.

Also check out the Least Common Multiple of 31409 and 31413