What is the Greatest Common Factor of 1900 and 1910?

Greatest common factor (GCF) of 1900 and 1910 is 10.

GCF(1900,1910) = 10

We will now calculate the prime factors of 1900 and 1910, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1900 and 1910.

How to find the GCF of 1900 and 1910?

We will first find the prime factorization of 1900 and 1910. After we will calculate the factors of 1900 and 1910 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 1910

Prime factors of 1910 are 2, 5, 191. Prime factorization of 1910 in exponential form is:

1910 = 2¹ × 5¹ × 191¹

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 1910

List of positive integer factors of 1910 that divides 1900 without a remainder.

1, 2, 5, 10, 191, 382, 955

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1900 and 1910. The biggest common factor number is the GCF number.
So the greatest common factor 1900 and 1910 is 10.

Also check out the Least Common Multiple of 1900 and 1910