What is the Greatest Common Factor of 19900 and 19909?

Greatest common factor (GCF) of 19900 and 19909 is 1.

GCF(19900,19909) = 1

We will now calculate the prime factors of 19900 and 19909, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19900 and 19909.

How to find the GCF of 19900 and 19909?

We will first find the prime factorization of 19900 and 19909. After we will calculate the factors of 19900 and 19909 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 19909

Prime factors of 19909 are 43, 463. Prime factorization of 19909 in exponential form is:

19909 = 43¹ × 463¹

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 19909

List of positive integer factors of 19909 that divides 19900 without a remainder.

1, 43, 463

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19900 and 19909. The biggest common factor number is the GCF number.
So the greatest common factor 19900 and 19909 is 1.

Also check out the Least Common Multiple of 19900 and 19909