What is the Greatest Common Factor of 17670 and 17689?

Greatest common factor (GCF) of 17670 and 17689 is 19.

GCF(17670,17689) = 19

We will now calculate the prime factors of 17670 and 17689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17670 and 17689.

How to find the GCF of 17670 and 17689?

We will first find the prime factorization of 17670 and 17689. After we will calculate the factors of 17670 and 17689 and find the biggest common factor number .

Step-1: Prime Factorization of 17670

Prime factors of 17670 are 2, 3, 5, 19, 31. Prime factorization of 17670 in exponential form is:

17670 = 2¹ × 3¹ × 5¹ × 19¹ × 31¹

Step-2: Prime Factorization of 17689

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

17689 = 7² × 19²

Step-3: Factors of 17670

List of positive integer factors of 17670 that divides 17670 without a remainder.

1, 2, 3, 5, 6, 10, 15, 19, 30, 31, 38, 57, 62, 93, 95, 114, 155, 186, 190, 285, 310, 465, 570, 589, 930, 1178, 1767, 2945, 3534, 5890, 8835

Step-4: Factors of 17689

List of positive integer factors of 17689 that divides 17670 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17670 and 17689. The biggest common factor number is the GCF number.
So the greatest common factor 17670 and 17689 is 19.

Also check out the Least Common Multiple of 17670 and 17689