What is the Greatest Common Factor of 13946 and 13965?

Greatest common factor (GCF) of 13946 and 13965 is 19.

GCF(13946,13965) = 19

We will now calculate the prime factors of 13946 and 13965, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13946 and 13965.

How to find the GCF of 13946 and 13965?

We will first find the prime factorization of 13946 and 13965. After we will calculate the factors of 13946 and 13965 and find the biggest common factor number .

Step-1: Prime Factorization of 13946

Prime factors of 13946 are 2, 19, 367. Prime factorization of 13946 in exponential form is:

13946 = 2¹ × 19¹ × 367¹

Step-2: Prime Factorization of 13965

Prime factors of 13965 are 3, 5, 7, 19. Prime factorization of 13965 in exponential form is:

13965 = 3¹ × 5¹ × 7² × 19¹

Step-3: Factors of 13946

List of positive integer factors of 13946 that divides 13946 without a remainder.

1, 2, 19, 38, 367, 734, 6973

Step-4: Factors of 13965

List of positive integer factors of 13965 that divides 13946 without a remainder.

1, 3, 5, 7, 15, 19, 21, 35, 49, 57, 95, 105, 133, 147, 245, 285, 399, 665, 735, 931, 1995, 2793, 4655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13946 and 13965. The biggest common factor number is the GCF number.
So the greatest common factor 13946 and 13965 is 19.

Also check out the Least Common Multiple of 13946 and 13965