What is the Greatest Common Factor of 13670 and 13690?

Greatest common factor (GCF) of 13670 and 13690 is 10.

GCF(13670,13690) = 10

We will now calculate the prime factors of 13670 and 13690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13670 and 13690.

How to find the GCF of 13670 and 13690?

We will first find the prime factorization of 13670 and 13690. After we will calculate the factors of 13670 and 13690 and find the biggest common factor number .

Step-1: Prime Factorization of 13670

Prime factors of 13670 are 2, 5, 1367. Prime factorization of 13670 in exponential form is:

13670 = 2¹ × 5¹ × 1367¹

Step-2: Prime Factorization of 13690

Prime factors of 13690 are 2, 5, 37. Prime factorization of 13690 in exponential form is:

13690 = 2¹ × 5¹ × 37²

Step-3: Factors of 13670

List of positive integer factors of 13670 that divides 13670 without a remainder.

1, 2, 5, 10, 1367, 2734, 6835

Step-4: Factors of 13690

List of positive integer factors of 13690 that divides 13670 without a remainder.

1, 2, 5, 10, 37, 74, 185, 370, 1369, 2738, 6845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13670 and 13690. The biggest common factor number is the GCF number.
So the greatest common factor 13670 and 13690 is 10.

Also check out the Least Common Multiple of 13670 and 13690