What is the Greatest Common Factor of 1854 and 1872?

Greatest common factor (GCF) of 1854 and 1872 is 18.

GCF(1854,1872) = 18

We will now calculate the prime factors of 1854 and 1872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1854 and 1872.

How to find the GCF of 1854 and 1872?

We will first find the prime factorization of 1854 and 1872. After we will calculate the factors of 1854 and 1872 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 1872

Prime factors of 1872 are 2, 3, 13. Prime factorization of 1872 in exponential form is:

1872 = 2⁴ × 3² × 13¹

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 1872

List of positive integer factors of 1872 that divides 1854 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1854 and 1872. The biggest common factor number is the GCF number.
So the greatest common factor 1854 and 1872 is 18.

Also check out the Least Common Multiple of 1854 and 1872