What is the Greatest Common Factor of 17214 and 17234?

Greatest common factor (GCF) of 17214 and 17234 is 2.

GCF(17214,17234) = 2

We will now calculate the prime factors of 17214 and 17234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17214 and 17234.

How to find the GCF of 17214 and 17234?

We will first find the prime factorization of 17214 and 17234. After we will calculate the factors of 17214 and 17234 and find the biggest common factor number .

Step-1: Prime Factorization of 17214

Prime factors of 17214 are 2, 3, 19, 151. Prime factorization of 17214 in exponential form is:

17214 = 2¹ × 3¹ × 19¹ × 151¹

Step-2: Prime Factorization of 17234

Prime factors of 17234 are 2, 7, 1231. Prime factorization of 17234 in exponential form is:

17234 = 2¹ × 7¹ × 1231¹

Step-3: Factors of 17214

List of positive integer factors of 17214 that divides 17214 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 151, 302, 453, 906, 2869, 5738, 8607

Step-4: Factors of 17234

List of positive integer factors of 17234 that divides 17214 without a remainder.

1, 2, 7, 14, 1231, 2462, 8617

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17214 and 17234. The biggest common factor number is the GCF number.
So the greatest common factor 17214 and 17234 is 2.

Also check out the Least Common Multiple of 17214 and 17234