What is the Greatest Common Factor of 1896 and 1900?

Greatest common factor (GCF) of 1896 and 1900 is 4.

GCF(1896,1900) = 4

We will now calculate the prime factors of 1896 and 1900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1896 and 1900.

How to find the GCF of 1896 and 1900?

We will first find the prime factorization of 1896 and 1900. After we will calculate the factors of 1896 and 1900 and find the biggest common factor number .

Step-1: Prime Factorization of 1896

Prime factors of 1896 are 2, 3, 79. Prime factorization of 1896 in exponential form is:

1896 = 2³ × 3¹ × 79¹

Step-2: Prime Factorization of 1900

Prime factors of 1900 are 2, 5, 19. Prime factorization of 1900 in exponential form is:

1900 = 2² × 5² × 19¹

Step-3: Factors of 1896

List of positive integer factors of 1896 that divides 1896 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 79, 158, 237, 316, 474, 632, 948

Step-4: Factors of 1900

List of positive integer factors of 1900 that divides 1896 without a remainder.

1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475, 950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1896 and 1900. The biggest common factor number is the GCF number.
So the greatest common factor 1896 and 1900 is 4.

Also check out the Least Common Multiple of 1896 and 1900