What is the Greatest Common Factor of 6409 and 6414?

Greatest common factor (GCF) of 6409 and 6414 is 1.

GCF(6409,6414) = 1

We will now calculate the prime factors of 6409 and 6414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6409 and 6414.

How to find the GCF of 6409 and 6414?

We will first find the prime factorization of 6409 and 6414. After we will calculate the factors of 6409 and 6414 and find the biggest common factor number .

Step-1: Prime Factorization of 6409

Prime factors of 6409 are 13, 17, 29. Prime factorization of 6409 in exponential form is:

6409 = 13¹ × 17¹ × 29¹

Step-2: Prime Factorization of 6414

Prime factors of 6414 are 2, 3, 1069. Prime factorization of 6414 in exponential form is:

6414 = 2¹ × 3¹ × 1069¹

Step-3: Factors of 6409

List of positive integer factors of 6409 that divides 6409 without a remainder.

1, 13, 17, 29, 221, 377, 493

Step-4: Factors of 6414

List of positive integer factors of 6414 that divides 6409 without a remainder.

1, 2, 3, 6, 1069, 2138, 3207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6409 and 6414. The biggest common factor number is the GCF number.
So the greatest common factor 6409 and 6414 is 1.

Also check out the Least Common Multiple of 6409 and 6414