What is the Greatest Common Factor of 17685 and 17697?

Greatest common factor (GCF) of 17685 and 17697 is 3.

GCF(17685,17697) = 3

We will now calculate the prime factors of 17685 and 17697, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17685 and 17697.

How to find the GCF of 17685 and 17697?

We will first find the prime factorization of 17685 and 17697. After we will calculate the factors of 17685 and 17697 and find the biggest common factor number .

Step-1: Prime Factorization of 17685

Prime factors of 17685 are 3, 5, 131. Prime factorization of 17685 in exponential form is:

17685 = 3³ × 5¹ × 131¹

Step-2: 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-3: Factors of 17685

List of positive integer factors of 17685 that divides 17685 without a remainder.

1, 3, 5, 9, 15, 27, 45, 131, 135, 393, 655, 1179, 1965, 3537, 5895

Step-4: Factors of 17697

List of positive integer factors of 17697 that divides 17685 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17685 and 17697. The biggest common factor number is the GCF number.
So the greatest common factor 17685 and 17697 is 3.

Also check out the Least Common Multiple of 17685 and 17697