What is the Greatest Common Factor of 19900 and 19910?

Greatest common factor (GCF) of 19900 and 19910 is 10.

GCF(19900,19910) = 10

We will now calculate the prime factors of 19900 and 19910, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19900 and 19910.

How to find the GCF of 19900 and 19910?

We will first find the prime factorization of 19900 and 19910. After we will calculate the factors of 19900 and 19910 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 19910

Prime factors of 19910 are 2, 5, 11, 181. Prime factorization of 19910 in exponential form is:

19910 = 2¹ × 5¹ × 11¹ × 181¹

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 19910

List of positive integer factors of 19910 that divides 19900 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110, 181, 362, 905, 1810, 1991, 3982, 9955

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19900 and 19910. The biggest common factor number is the GCF number.
So the greatest common factor 19900 and 19910 is 10.

Also check out the Least Common Multiple of 19900 and 19910