What is the Greatest Common Factor of 1914 and 1920?

Greatest common factor (GCF) of 1914 and 1920 is 6.

GCF(1914,1920) = 6

We will now calculate the prime factors of 1914 and 1920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1914 and 1920.

How to find the GCF of 1914 and 1920?

We will first find the prime factorization of 1914 and 1920. After we will calculate the factors of 1914 and 1920 and find the biggest common factor number .

Step-1: Prime Factorization of 1914

Prime factors of 1914 are 2, 3, 11, 29. Prime factorization of 1914 in exponential form is:

1914 = 2¹ × 3¹ × 11¹ × 29¹

Step-2: 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-3: Factors of 1914

List of positive integer factors of 1914 that divides 1914 without a remainder.

1, 2, 3, 6, 11, 22, 29, 33, 58, 66, 87, 174, 319, 638, 957

Step-4: Factors of 1920

List of positive integer factors of 1920 that divides 1914 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1914 and 1920. The biggest common factor number is the GCF number.
So the greatest common factor 1914 and 1920 is 6.

Also check out the Least Common Multiple of 1914 and 1920