What is the Greatest Common Factor of 17314 and 17325?

Greatest common factor (GCF) of 17314 and 17325 is 11.

GCF(17314,17325) = 11

We will now calculate the prime factors of 17314 and 17325, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17314 and 17325.

How to find the GCF of 17314 and 17325?

We will first find the prime factorization of 17314 and 17325. After we will calculate the factors of 17314 and 17325 and find the biggest common factor number .

Step-1: Prime Factorization of 17314

Prime factors of 17314 are 2, 11, 787. Prime factorization of 17314 in exponential form is:

17314 = 2¹ × 11¹ × 787¹

Step-2: Prime Factorization of 17325

Prime factors of 17325 are 3, 5, 7, 11. Prime factorization of 17325 in exponential form is:

17325 = 3² × 5² × 7¹ × 11¹

Step-3: Factors of 17314

List of positive integer factors of 17314 that divides 17314 without a remainder.

1, 2, 11, 22, 787, 1574, 8657

Step-4: Factors of 17325

List of positive integer factors of 17325 that divides 17314 without a remainder.

1, 3, 5, 7, 9, 11, 15, 21, 25, 33, 35, 45, 55, 63, 75, 77, 99, 105, 165, 175, 225, 231, 275, 315, 385, 495, 525, 693, 825, 1155, 1575, 1925, 2475, 3465, 5775

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17314 and 17325. The biggest common factor number is the GCF number.
So the greatest common factor 17314 and 17325 is 11.

Also check out the Least Common Multiple of 17314 and 17325