What is the Greatest Common Factor of 9900 and 9919?

Greatest common factor (GCF) of 9900 and 9919 is 1.

GCF(9900,9919) = 1

We will now calculate the prime factors of 9900 and 9919, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9900 and 9919.

How to find the GCF of 9900 and 9919?

We will first find the prime factorization of 9900 and 9919. After we will calculate the factors of 9900 and 9919 and find the biggest common factor number .

Step-1: Prime Factorization of 9900

Prime factors of 9900 are 2, 3, 5, 11. Prime factorization of 9900 in exponential form is:

9900 = 2² × 3² × 5² × 11¹

Step-2: Prime Factorization of 9919

Prime factors of 9919 are 7, 13, 109. Prime factorization of 9919 in exponential form is:

9919 = 7¹ × 13¹ × 109¹

Step-3: Factors of 9900

List of positive integer factors of 9900 that divides 9900 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950

Step-4: Factors of 9919

List of positive integer factors of 9919 that divides 9900 without a remainder.

1, 7, 13, 91, 109, 763, 1417

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9900 and 9919. The biggest common factor number is the GCF number.
So the greatest common factor 9900 and 9919 is 1.

Also check out the Least Common Multiple of 9900 and 9919