What is the Greatest Common Factor of 1834 and 1854?

Greatest common factor (GCF) of 1834 and 1854 is 2.

GCF(1834,1854) = 2

We will now calculate the prime factors of 1834 and 1854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1834 and 1854.

How to find the GCF of 1834 and 1854?

We will first find the prime factorization of 1834 and 1854. After we will calculate the factors of 1834 and 1854 and find the biggest common factor number .

Step-1: Prime Factorization of 1834

Prime factors of 1834 are 2, 7, 131. Prime factorization of 1834 in exponential form is:

1834 = 2¹ × 7¹ × 131¹

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 1834

List of positive integer factors of 1834 that divides 1834 without a remainder.

1, 2, 7, 14, 131, 262, 917

Step-4: Factors of 1854

List of positive integer factors of 1854 that divides 1834 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 1834 and 1854. The biggest common factor number is the GCF number.
So the greatest common factor 1834 and 1854 is 2.

Also check out the Least Common Multiple of 1834 and 1854