What is the Greatest Common Factor of 17697 and 17709?

Greatest common factor (GCF) of 17697 and 17709 is 3.

GCF(17697,17709) = 3

We will now calculate the prime factors of 17697 and 17709, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17697 and 17709.

How to find the GCF of 17697 and 17709?

We will first find the prime factorization of 17697 and 17709. After we will calculate the factors of 17697 and 17709 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 17709

Prime factors of 17709 are 3, 5903. Prime factorization of 17709 in exponential form is:

17709 = 3¹ × 5903¹

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 17709

List of positive integer factors of 17709 that divides 17697 without a remainder.

1, 3, 5903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17697 and 17709. The biggest common factor number is the GCF number.
So the greatest common factor 17697 and 17709 is 3.

Also check out the Least Common Multiple of 17697 and 17709