What is the Greatest Common Factor of 17214 and 17233?

Greatest common factor (GCF) of 17214 and 17233 is 19.

GCF(17214,17233) = 19

We will now calculate the prime factors of 17214 and 17233, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17214 and 17233.

How to find the GCF of 17214 and 17233?

We will first find the prime factorization of 17214 and 17233. After we will calculate the factors of 17214 and 17233 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 17233

Prime factors of 17233 are 19, 907. Prime factorization of 17233 in exponential form is:

17233 = 19¹ × 907¹

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 17233

List of positive integer factors of 17233 that divides 17214 without a remainder.

1, 19, 907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17214 and 17233. The biggest common factor number is the GCF number.
So the greatest common factor 17214 and 17233 is 19.

Also check out the Least Common Multiple of 17214 and 17233