What is the Greatest Common Factor of 1836 and 1854?

Greatest common factor (GCF) of 1836 and 1854 is 18.

GCF(1836,1854) = 18

We will now calculate the prime factors of 1836 and 1854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1836 and 1854.

How to find the GCF of 1836 and 1854?

We will first find the prime factorization of 1836 and 1854. After we will calculate the factors of 1836 and 1854 and find the biggest common factor number .

Step-1: Prime Factorization of 1836

Prime factors of 1836 are 2, 3, 17. Prime factorization of 1836 in exponential form is:

1836 = 2² × 3³ × 17¹

Step-2: 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-3: Factors of 1836

List of positive integer factors of 1836 that divides 1836 without a remainder.

1, 2, 3, 4, 6, 9, 12, 17, 18, 27, 34, 36, 51, 54, 68, 102, 108, 153, 204, 306, 459, 612, 918

Step-4: Factors of 1854

List of positive integer factors of 1854 that divides 1836 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1836 and 1854. The biggest common factor number is the GCF number.
So the greatest common factor 1836 and 1854 is 18.

Also check out the Least Common Multiple of 1836 and 1854