What is the Greatest Common Factor of 1920 and 1938?

Greatest common factor (GCF) of 1920 and 1938 is 6.

GCF(1920,1938) = 6

We will now calculate the prime factors of 1920 and 1938, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1920 and 1938.

How to find the GCF of 1920 and 1938?

We will first find the prime factorization of 1920 and 1938. After we will calculate the factors of 1920 and 1938 and find the biggest common factor number .

Step-1: Prime Factorization of 1920

Prime factors of 1920 are 2, 3, 5. Prime factorization of 1920 in exponential form is:

1920 = 2⁷ × 3¹ × 5¹

Step-2: Prime Factorization of 1938

Prime factors of 1938 are 2, 3, 17, 19. Prime factorization of 1938 in exponential form is:

1938 = 2¹ × 3¹ × 17¹ × 19¹

Step-3: Factors of 1920

List of positive integer factors of 1920 that divides 1920 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960

Step-4: Factors of 1938

List of positive integer factors of 1938 that divides 1920 without a remainder.

1, 2, 3, 6, 17, 19, 34, 38, 51, 57, 102, 114, 323, 646, 969

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1920 and 1938. The biggest common factor number is the GCF number.
So the greatest common factor 1920 and 1938 is 6.

Also check out the Least Common Multiple of 1920 and 1938