What is the Greatest Common Factor of 20919 and 20938?

Greatest common factor (GCF) of 20919 and 20938 is 19.

GCF(20919,20938) = 19

We will now calculate the prime factors of 20919 and 20938, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20919 and 20938.

How to find the GCF of 20919 and 20938?

We will first find the prime factorization of 20919 and 20938. After we will calculate the factors of 20919 and 20938 and find the biggest common factor number .

Step-1: Prime Factorization of 20919

Prime factors of 20919 are 3, 19, 367. Prime factorization of 20919 in exponential form is:

20919 = 3¹ × 19¹ × 367¹

Step-2: Prime Factorization of 20938

Prime factors of 20938 are 2, 19, 29. Prime factorization of 20938 in exponential form is:

20938 = 2¹ × 19² × 29¹

Step-3: Factors of 20919

List of positive integer factors of 20919 that divides 20919 without a remainder.

1, 3, 19, 57, 367, 1101, 6973

Step-4: Factors of 20938

List of positive integer factors of 20938 that divides 20919 without a remainder.

1, 2, 19, 29, 38, 58, 361, 551, 722, 1102, 10469

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20919 and 20938. The biggest common factor number is the GCF number.
So the greatest common factor 20919 and 20938 is 19.

Also check out the Least Common Multiple of 20919 and 20938