What is the Greatest Common Factor of 1875 and 1890?

Greatest common factor (GCF) of 1875 and 1890 is 15.

GCF(1875,1890) = 15

We will now calculate the prime factors of 1875 and 1890, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1875 and 1890.

How to find the GCF of 1875 and 1890?

We will first find the prime factorization of 1875 and 1890. After we will calculate the factors of 1875 and 1890 and find the biggest common factor number .

Step-1: Prime Factorization of 1875

Prime factors of 1875 are 3, 5. Prime factorization of 1875 in exponential form is:

1875 = 3¹ × 5⁴

Step-2: 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-3: Factors of 1875

List of positive integer factors of 1875 that divides 1875 without a remainder.

1, 3, 5, 15, 25, 75, 125, 375, 625

Step-4: Factors of 1890

List of positive integer factors of 1890 that divides 1875 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1875 and 1890. The biggest common factor number is the GCF number.
So the greatest common factor 1875 and 1890 is 15.

Also check out the Least Common Multiple of 1875 and 1890