What is the Greatest Common Factor of 17314 and 17320?

Greatest common factor (GCF) of 17314 and 17320 is 2.

GCF(17314,17320) = 2

We will now calculate the prime factors of 17314 and 17320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17314 and 17320.

How to find the GCF of 17314 and 17320?

We will first find the prime factorization of 17314 and 17320. After we will calculate the factors of 17314 and 17320 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 17320

Prime factors of 17320 are 2, 5, 433. Prime factorization of 17320 in exponential form is:

17320 = 2³ × 5¹ × 433¹

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 17320

List of positive integer factors of 17320 that divides 17314 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 433, 866, 1732, 2165, 3464, 4330, 8660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17314 and 17320. The biggest common factor number is the GCF number.
So the greatest common factor 17314 and 17320 is 2.

Also check out the Least Common Multiple of 17314 and 17320