What is the Greatest Common Factor of 1890 and 1904?

Greatest common factor (GCF) of 1890 and 1904 is 14.

GCF(1890,1904) = 14

We will now calculate the prime factors of 1890 and 1904, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1890 and 1904.

How to find the GCF of 1890 and 1904?

We will first find the prime factorization of 1890 and 1904. After we will calculate the factors of 1890 and 1904 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 1904

Prime factors of 1904 are 2, 7, 17. Prime factorization of 1904 in exponential form is:

1904 = 2⁴ × 7¹ × 17¹

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 1904

List of positive integer factors of 1904 that divides 1890 without a remainder.

1, 2, 4, 7, 8, 14, 16, 17, 28, 34, 56, 68, 112, 119, 136, 238, 272, 476, 952

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1890 and 1904. The biggest common factor number is the GCF number.
So the greatest common factor 1890 and 1904 is 14.

Also check out the Least Common Multiple of 1890 and 1904