What is the Greatest Common Factor of 19994 and 20007?

Greatest common factor (GCF) of 19994 and 20007 is 13.

GCF(19994,20007) = 13

We will now calculate the prime factors of 19994 and 20007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19994 and 20007.

How to find the GCF of 19994 and 20007?

We will first find the prime factorization of 19994 and 20007. After we will calculate the factors of 19994 and 20007 and find the biggest common factor number .

Step-1: Prime Factorization of 19994

Prime factors of 19994 are 2, 13, 769. Prime factorization of 19994 in exponential form is:

19994 = 2¹ × 13¹ × 769¹

Step-2: Prime Factorization of 20007

Prime factors of 20007 are 3, 13, 19. Prime factorization of 20007 in exponential form is:

20007 = 3⁴ × 13¹ × 19¹

Step-3: Factors of 19994

List of positive integer factors of 19994 that divides 19994 without a remainder.

1, 2, 13, 26, 769, 1538, 9997

Step-4: Factors of 20007

List of positive integer factors of 20007 that divides 19994 without a remainder.

1, 3, 9, 13, 19, 27, 39, 57, 81, 117, 171, 247, 351, 513, 741, 1053, 1539, 2223, 6669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19994 and 20007. The biggest common factor number is the GCF number.
So the greatest common factor 19994 and 20007 is 13.

Also check out the Least Common Multiple of 19994 and 20007