What is the Greatest Common Factor of 39800 and 39808?

Greatest common factor (GCF) of 39800 and 39808 is 8.

GCF(39800,39808) = 8

We will now calculate the prime factors of 39800 and 39808, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39800 and 39808.

How to find the GCF of 39800 and 39808?

We will first find the prime factorization of 39800 and 39808. After we will calculate the factors of 39800 and 39808 and find the biggest common factor number .

Step-1: Prime Factorization of 39800

Prime factors of 39800 are 2, 5, 199. Prime factorization of 39800 in exponential form is:

39800 = 2³ × 5² × 199¹

Step-2: Prime Factorization of 39808

Prime factors of 39808 are 2, 311. Prime factorization of 39808 in exponential form is:

39808 = 2⁷ × 311¹

Step-3: Factors of 39800

List of positive integer factors of 39800 that divides 39800 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 199, 200, 398, 796, 995, 1592, 1990, 3980, 4975, 7960, 9950, 19900

Step-4: Factors of 39808

List of positive integer factors of 39808 that divides 39800 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 311, 622, 1244, 2488, 4976, 9952, 19904

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39800 and 39808. The biggest common factor number is the GCF number.
So the greatest common factor 39800 and 39808 is 8.

Also check out the Least Common Multiple of 39800 and 39808