What is the Greatest Common Factor of 3840 and 3854?

Greatest common factor (GCF) of 3840 and 3854 is 2.

GCF(3840,3854) = 2

We will now calculate the prime factors of 3840 and 3854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3840 and 3854.

How to find the GCF of 3840 and 3854?

We will first find the prime factorization of 3840 and 3854. After we will calculate the factors of 3840 and 3854 and find the biggest common factor number .

Step-1: Prime Factorization of 3840

Prime factors of 3840 are 2, 3, 5. Prime factorization of 3840 in exponential form is:

3840 = 2⁸ × 3¹ × 5¹

Step-2: 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-3: Factors of 3840

List of positive integer factors of 3840 that divides 3840 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 640, 768, 960, 1280, 1920

Step-4: Factors of 3854

List of positive integer factors of 3854 that divides 3840 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3840 and 3854. The biggest common factor number is the GCF number.
So the greatest common factor 3840 and 3854 is 2.

Also check out the Least Common Multiple of 3840 and 3854