What is the Greatest Common Factor of 19900 and 19906?

Greatest common factor (GCF) of 19900 and 19906 is 2.

GCF(19900,19906) = 2

We will now calculate the prime factors of 19900 and 19906, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19900 and 19906.

How to find the GCF of 19900 and 19906?

We will first find the prime factorization of 19900 and 19906. After we will calculate the factors of 19900 and 19906 and find the biggest common factor number .

Step-1: Prime Factorization of 19900

Prime factors of 19900 are 2, 5, 199. Prime factorization of 19900 in exponential form is:

19900 = 2² × 5² × 199¹

Step-2: Prime Factorization of 19906

Prime factors of 19906 are 2, 37, 269. Prime factorization of 19906 in exponential form is:

19906 = 2¹ × 37¹ × 269¹

Step-3: Factors of 19900

List of positive integer factors of 19900 that divides 19900 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 199, 398, 796, 995, 1990, 3980, 4975, 9950

Step-4: Factors of 19906

List of positive integer factors of 19906 that divides 19900 without a remainder.

1, 2, 37, 74, 269, 538, 9953

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19900 and 19906. The biggest common factor number is the GCF number.
So the greatest common factor 19900 and 19906 is 2.

Also check out the Least Common Multiple of 19900 and 19906