What is the Greatest Common Factor of 39800 and 39805?

Greatest common factor (GCF) of 39800 and 39805 is 5.

GCF(39800,39805) = 5

We will now calculate the prime factors of 39800 and 39805, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39800 and 39805.

How to find the GCF of 39800 and 39805?

We will first find the prime factorization of 39800 and 39805. After we will calculate the factors of 39800 and 39805 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 39805

Prime factors of 39805 are 5, 19, 419. Prime factorization of 39805 in exponential form is:

39805 = 5¹ × 19¹ × 419¹

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 39805

List of positive integer factors of 39805 that divides 39800 without a remainder.

1, 5, 19, 95, 419, 2095, 7961

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39800 and 39805. The biggest common factor number is the GCF number.
So the greatest common factor 39800 and 39805 is 5.

Also check out the Least Common Multiple of 39800 and 39805