What is the Greatest Common Factor of 1890 and 1900?

Greatest common factor (GCF) of 1890 and 1900 is 10.

GCF(1890,1900) = 10

We will now calculate the prime factors of 1890 and 1900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1890 and 1900.

How to find the GCF of 1890 and 1900?

We will first find the prime factorization of 1890 and 1900. After we will calculate the factors of 1890 and 1900 and find the biggest common factor number .

Step-1: Prime Factorization of 1890

Prime factors of 1890 are 2, 3, 5, 7. Prime factorization of 1890 in exponential form is:

1890 = 2¹ × 3³ × 5¹ × 7¹

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 1890

List of positive integer factors of 1890 that divides 1890 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945

Step-4: Factors of 1900

List of positive integer factors of 1900 that divides 1890 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 1890 and 1900. The biggest common factor number is the GCF number.
So the greatest common factor 1890 and 1900 is 10.

Also check out the Least Common Multiple of 1890 and 1900