What is the Greatest Common Factor of 1890 and 1908?

Greatest common factor (GCF) of 1890 and 1908 is 18.

GCF(1890,1908) = 18

We will now calculate the prime factors of 1890 and 1908, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1890 and 1908.

How to find the GCF of 1890 and 1908?

We will first find the prime factorization of 1890 and 1908. After we will calculate the factors of 1890 and 1908 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 1908

Prime factors of 1908 are 2, 3, 53. Prime factorization of 1908 in exponential form is:

1908 = 2² × 3² × 53¹

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 1908

List of positive integer factors of 1908 that divides 1890 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 53, 106, 159, 212, 318, 477, 636, 954

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1890 and 1908. The biggest common factor number is the GCF number.
So the greatest common factor 1890 and 1908 is 18.

Also check out the Least Common Multiple of 1890 and 1908