What is the Greatest Common Factor of 17697 and 17714?

Greatest common factor (GCF) of 17697 and 17714 is 17.

GCF(17697,17714) = 17

We will now calculate the prime factors of 17697 and 17714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17697 and 17714.

How to find the GCF of 17697 and 17714?

We will first find the prime factorization of 17697 and 17714. After we will calculate the factors of 17697 and 17714 and find the biggest common factor number .

Step-1: Prime Factorization of 17697

Prime factors of 17697 are 3, 17, 347. Prime factorization of 17697 in exponential form is:

17697 = 3¹ × 17¹ × 347¹

Step-2: Prime Factorization of 17714

Prime factors of 17714 are 2, 17, 521. Prime factorization of 17714 in exponential form is:

17714 = 2¹ × 17¹ × 521¹

Step-3: Factors of 17697

List of positive integer factors of 17697 that divides 17697 without a remainder.

1, 3, 17, 51, 347, 1041, 5899

Step-4: Factors of 17714

List of positive integer factors of 17714 that divides 17697 without a remainder.

1, 2, 17, 34, 521, 1042, 8857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17697 and 17714. The biggest common factor number is the GCF number.
So the greatest common factor 17697 and 17714 is 17.

Also check out the Least Common Multiple of 17697 and 17714