What is the Greatest Common Factor of 20919 and 20928?

Greatest common factor (GCF) of 20919 and 20928 is 3.

GCF(20919,20928) = 3

We will now calculate the prime factors of 20919 and 20928, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20919 and 20928.

How to find the GCF of 20919 and 20928?

We will first find the prime factorization of 20919 and 20928. After we will calculate the factors of 20919 and 20928 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 20928

Prime factors of 20928 are 2, 3, 109. Prime factorization of 20928 in exponential form is:

20928 = 2⁶ × 3¹ × 109¹

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 20928

List of positive integer factors of 20928 that divides 20919 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 109, 192, 218, 327, 436, 654, 872, 1308, 1744, 2616, 3488, 5232, 6976, 10464

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20919 and 20928. The biggest common factor number is the GCF number.
So the greatest common factor 20919 and 20928 is 3.

Also check out the Least Common Multiple of 20919 and 20928