What is the Greatest Common Factor of 39800 and 39814?

Greatest common factor (GCF) of 39800 and 39814 is 2.

GCF(39800,39814) = 2

We will now calculate the prime factors of 39800 and 39814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39800 and 39814.

How to find the GCF of 39800 and 39814?

We will first find the prime factorization of 39800 and 39814. After we will calculate the factors of 39800 and 39814 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 39814

Prime factors of 39814 are 2, 17, 1171. Prime factorization of 39814 in exponential form is:

39814 = 2¹ × 17¹ × 1171¹

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 39814

List of positive integer factors of 39814 that divides 39800 without a remainder.

1, 2, 17, 34, 1171, 2342, 19907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39800 and 39814. The biggest common factor number is the GCF number.
So the greatest common factor 39800 and 39814 is 2.

Also check out the Least Common Multiple of 39800 and 39814