What is the Greatest Common Factor of 17409 and 17414?

Greatest common factor (GCF) of 17409 and 17414 is 1.

GCF(17409,17414) = 1

We will now calculate the prime factors of 17409 and 17414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17409 and 17414.

How to find the GCF of 17409 and 17414?

We will first find the prime factorization of 17409 and 17414. After we will calculate the factors of 17409 and 17414 and find the biggest common factor number .

Step-1: Prime Factorization of 17409

Prime factors of 17409 are 3, 7, 829. Prime factorization of 17409 in exponential form is:

17409 = 3¹ × 7¹ × 829¹

Step-2: Prime Factorization of 17414

Prime factors of 17414 are 2, 8707. Prime factorization of 17414 in exponential form is:

17414 = 2¹ × 8707¹

Step-3: Factors of 17409

List of positive integer factors of 17409 that divides 17409 without a remainder.

1, 3, 7, 21, 829, 2487, 5803

Step-4: Factors of 17414

List of positive integer factors of 17414 that divides 17409 without a remainder.

1, 2, 8707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17409 and 17414. The biggest common factor number is the GCF number.
So the greatest common factor 17409 and 17414 is 1.

Also check out the Least Common Multiple of 17409 and 17414