What is the Greatest Common Factor of 3854 and 3872?

Greatest common factor (GCF) of 3854 and 3872 is 2.

GCF(3854,3872) = 2

We will now calculate the prime factors of 3854 and 3872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3854 and 3872.

How to find the GCF of 3854 and 3872?

We will first find the prime factorization of 3854 and 3872. After we will calculate the factors of 3854 and 3872 and find the biggest common factor number .

Step-1: Prime Factorization of 3854

Prime factors of 3854 are 2, 41, 47. Prime factorization of 3854 in exponential form is:

3854 = 2¹ × 41¹ × 47¹

Step-2: Prime Factorization of 3872

Prime factors of 3872 are 2, 11. Prime factorization of 3872 in exponential form is:

3872 = 2⁵ × 11²

Step-3: Factors of 3854

List of positive integer factors of 3854 that divides 3854 without a remainder.

1, 2, 41, 47, 82, 94, 1927

Step-4: Factors of 3872

List of positive integer factors of 3872 that divides 3854 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 121, 176, 242, 352, 484, 968, 1936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3854 and 3872. The biggest common factor number is the GCF number.
So the greatest common factor 3854 and 3872 is 2.

Also check out the Least Common Multiple of 3854 and 3872