What is the Greatest Common Factor of 17414 and 17422?

Greatest common factor (GCF) of 17414 and 17422 is 2.

GCF(17414,17422) = 2

We will now calculate the prime factors of 17414 and 17422, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17414 and 17422.

How to find the GCF of 17414 and 17422?

We will first find the prime factorization of 17414 and 17422. After we will calculate the factors of 17414 and 17422 and find the biggest common factor number .

Step-1: Prime Factorization of 17414

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

17414 = 2¹ × 8707¹

Step-2: Prime Factorization of 17422

Prime factors of 17422 are 2, 31, 281. Prime factorization of 17422 in exponential form is:

17422 = 2¹ × 31¹ × 281¹

Step-3: Factors of 17414

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

1, 2, 8707

Step-4: Factors of 17422

List of positive integer factors of 17422 that divides 17414 without a remainder.

1, 2, 31, 62, 281, 562, 8711

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17414 and 17422. The biggest common factor number is the GCF number.
So the greatest common factor 17414 and 17422 is 2.

Also check out the Least Common Multiple of 17414 and 17422