What is the Greatest Common Factor of 38800 and 38814?

Greatest common factor (GCF) of 38800 and 38814 is 2.

GCF(38800,38814) = 2

We will now calculate the prime factors of 38800 and 38814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38800 and 38814.

How to find the GCF of 38800 and 38814?

We will first find the prime factorization of 38800 and 38814. After we will calculate the factors of 38800 and 38814 and find the biggest common factor number .

Step-1: Prime Factorization of 38800

Prime factors of 38800 are 2, 5, 97. Prime factorization of 38800 in exponential form is:

38800 = 2⁴ × 5² × 97¹

Step-2: Prime Factorization of 38814

Prime factors of 38814 are 2, 3, 6469. Prime factorization of 38814 in exponential form is:

38814 = 2¹ × 3¹ × 6469¹

Step-3: Factors of 38800

List of positive integer factors of 38800 that divides 38800 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 97, 100, 194, 200, 388, 400, 485, 776, 970, 1552, 1940, 2425, 3880, 4850, 7760, 9700, 19400

Step-4: Factors of 38814

List of positive integer factors of 38814 that divides 38800 without a remainder.

1, 2, 3, 6, 6469, 12938, 19407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38800 and 38814. The biggest common factor number is the GCF number.
So the greatest common factor 38800 and 38814 is 2.

Also check out the Least Common Multiple of 38800 and 38814