What is the Greatest Common Factor of 1854 and 1870?

Greatest common factor (GCF) of 1854 and 1870 is 2.

GCF(1854,1870) = 2

We will now calculate the prime factors of 1854 and 1870, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1854 and 1870.

How to find the GCF of 1854 and 1870?

We will first find the prime factorization of 1854 and 1870. After we will calculate the factors of 1854 and 1870 and find the biggest common factor number .

Step-1: Prime Factorization of 1854

Prime factors of 1854 are 2, 3, 103. Prime factorization of 1854 in exponential form is:

1854 = 2¹ × 3² × 103¹

Step-2: Prime Factorization of 1870

Prime factors of 1870 are 2, 5, 11, 17. Prime factorization of 1870 in exponential form is:

1870 = 2¹ × 5¹ × 11¹ × 17¹

Step-3: Factors of 1854

List of positive integer factors of 1854 that divides 1854 without a remainder.

1, 2, 3, 6, 9, 18, 103, 206, 309, 618, 927

Step-4: Factors of 1870

List of positive integer factors of 1870 that divides 1854 without a remainder.

1, 2, 5, 10, 11, 17, 22, 34, 55, 85, 110, 170, 187, 374, 935

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1854 and 1870. The biggest common factor number is the GCF number.
So the greatest common factor 1854 and 1870 is 2.

Also check out the Least Common Multiple of 1854 and 1870