What is the Greatest Common Factor of 17697 and 17706?

Greatest common factor (GCF) of 17697 and 17706 is 3.

GCF(17697,17706) = 3

We will now calculate the prime factors of 17697 and 17706, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17697 and 17706.

How to find the GCF of 17697 and 17706?

We will first find the prime factorization of 17697 and 17706. After we will calculate the factors of 17697 and 17706 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 17706

Prime factors of 17706 are 2, 3, 13, 227. Prime factorization of 17706 in exponential form is:

17706 = 2¹ × 3¹ × 13¹ × 227¹

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 17706

List of positive integer factors of 17706 that divides 17697 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 227, 454, 681, 1362, 2951, 5902, 8853

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17697 and 17706. The biggest common factor number is the GCF number.
So the greatest common factor 17697 and 17706 is 3.

Also check out the Least Common Multiple of 17697 and 17706