What is the Greatest Common Factor of 1900 and 1919?

Greatest common factor (GCF) of 1900 and 1919 is 19.

GCF(1900,1919) = 19

We will now calculate the prime factors of 1900 and 1919, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1900 and 1919.

How to find the GCF of 1900 and 1919?

We will first find the prime factorization of 1900 and 1919. After we will calculate the factors of 1900 and 1919 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1919

Prime factors of 1919 are 19, 101. Prime factorization of 1919 in exponential form is:

1919 = 19¹ × 101¹

Step-3: Factors of 1900

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

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

Step-4: Factors of 1919

List of positive integer factors of 1919 that divides 1900 without a remainder.

1, 19, 101

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1900 and 1919. The biggest common factor number is the GCF number.
So the greatest common factor 1900 and 1919 is 19.

Also check out the Least Common Multiple of 1900 and 1919