What is the Greatest Common Factor of 3800 and 3814?

Greatest common factor (GCF) of 3800 and 3814 is 2.

GCF(3800,3814) = 2

We will now calculate the prime factors of 3800 and 3814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3800 and 3814.

How to find the GCF of 3800 and 3814?

We will first find the prime factorization of 3800 and 3814. After we will calculate the factors of 3800 and 3814 and find the biggest common factor number .

Step-1: Prime Factorization of 3800

Prime factors of 3800 are 2, 5, 19. Prime factorization of 3800 in exponential form is:

3800 = 2³ × 5² × 19¹

Step-2: Prime Factorization of 3814

Prime factors of 3814 are 2, 1907. Prime factorization of 3814 in exponential form is:

3814 = 2¹ × 1907¹

Step-3: Factors of 3800

List of positive integer factors of 3800 that divides 3800 without a remainder.

1, 2, 4, 5, 8, 10, 19, 20, 25, 38, 40, 50, 76, 95, 100, 152, 190, 200, 380, 475, 760, 950, 1900

Step-4: Factors of 3814

List of positive integer factors of 3814 that divides 3800 without a remainder.

1, 2, 1907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3800 and 3814. The biggest common factor number is the GCF number.
So the greatest common factor 3800 and 3814 is 2.

Also check out the Least Common Multiple of 3800 and 3814