What is the Greatest Common Factor of 17205 and 17214?

Greatest common factor (GCF) of 17205 and 17214 is 3.

GCF(17205,17214) = 3

We will now calculate the prime factors of 17205 and 17214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17205 and 17214.

How to find the GCF of 17205 and 17214?

We will first find the prime factorization of 17205 and 17214. After we will calculate the factors of 17205 and 17214 and find the biggest common factor number .

Step-1: Prime Factorization of 17205

Prime factors of 17205 are 3, 5, 31, 37. Prime factorization of 17205 in exponential form is:

17205 = 3¹ × 5¹ × 31¹ × 37¹

Step-2: 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-3: Factors of 17205

List of positive integer factors of 17205 that divides 17205 without a remainder.

1, 3, 5, 15, 31, 37, 93, 111, 155, 185, 465, 555, 1147, 3441, 5735

Step-4: Factors of 17214

List of positive integer factors of 17214 that divides 17205 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17205 and 17214. The biggest common factor number is the GCF number.
So the greatest common factor 17205 and 17214 is 3.

Also check out the Least Common Multiple of 17205 and 17214