What is the Greatest Common Factor of 17689 and 17708?

Greatest common factor (GCF) of 17689 and 17708 is 19.

GCF(17689,17708) = 19

We will now calculate the prime factors of 17689 and 17708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17689 and 17708.

How to find the GCF of 17689 and 17708?

We will first find the prime factorization of 17689 and 17708. After we will calculate the factors of 17689 and 17708 and find the biggest common factor number .

Step-1: Prime Factorization of 17689

Prime factors of 17689 are 7, 19. Prime factorization of 17689 in exponential form is:

17689 = 7² × 19²

Step-2: Prime Factorization of 17708

Prime factors of 17708 are 2, 19, 233. Prime factorization of 17708 in exponential form is:

17708 = 2² × 19¹ × 233¹

Step-3: Factors of 17689

List of positive integer factors of 17689 that divides 17689 without a remainder.

1, 7, 19, 49, 133, 361, 931, 2527

Step-4: Factors of 17708

List of positive integer factors of 17708 that divides 17689 without a remainder.

1, 2, 4, 19, 38, 76, 233, 466, 932, 4427, 8854

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17689 and 17708. The biggest common factor number is the GCF number.
So the greatest common factor 17689 and 17708 is 19.

Also check out the Least Common Multiple of 17689 and 17708