What is the Greatest Common Factor of 1905 and 1920?

Greatest common factor (GCF) of 1905 and 1920 is 15.

GCF(1905,1920) = 15

We will now calculate the prime factors of 1905 and 1920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1905 and 1920.

How to find the GCF of 1905 and 1920?

We will first find the prime factorization of 1905 and 1920. After we will calculate the factors of 1905 and 1920 and find the biggest common factor number .

Step-1: Prime Factorization of 1905

Prime factors of 1905 are 3, 5, 127. Prime factorization of 1905 in exponential form is:

1905 = 3¹ × 5¹ × 127¹

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 1905

List of positive integer factors of 1905 that divides 1905 without a remainder.

1, 3, 5, 15, 127, 381, 635

Step-4: Factors of 1920

List of positive integer factors of 1920 that divides 1905 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 1905 and 1920. The biggest common factor number is the GCF number.
So the greatest common factor 1905 and 1920 is 15.

Also check out the Least Common Multiple of 1905 and 1920