What is the Greatest Common Factor of 17312 and 17322?

Greatest common factor (GCF) of 17312 and 17322 is 2.

GCF(17312,17322) = 2

We will now calculate the prime factors of 17312 and 17322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17312 and 17322.

How to find the GCF of 17312 and 17322?

We will first find the prime factorization of 17312 and 17322. After we will calculate the factors of 17312 and 17322 and find the biggest common factor number .

Step-1: Prime Factorization of 17312

Prime factors of 17312 are 2, 541. Prime factorization of 17312 in exponential form is:

17312 = 2⁵ × 541¹

Step-2: Prime Factorization of 17322

Prime factors of 17322 are 2, 3, 2887. Prime factorization of 17322 in exponential form is:

17322 = 2¹ × 3¹ × 2887¹

Step-3: Factors of 17312

List of positive integer factors of 17312 that divides 17312 without a remainder.

1, 2, 4, 8, 16, 32, 541, 1082, 2164, 4328, 8656

Step-4: Factors of 17322

List of positive integer factors of 17322 that divides 17312 without a remainder.

1, 2, 3, 6, 2887, 5774, 8661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17312 and 17322. The biggest common factor number is the GCF number.
So the greatest common factor 17312 and 17322 is 2.

Also check out the Least Common Multiple of 17312 and 17322