What is the Greatest Common Factor of 9900 and 9905?

Greatest common factor (GCF) of 9900 and 9905 is 5.

GCF(9900,9905) = 5

We will now calculate the prime factors of 9900 and 9905, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9900 and 9905.

How to find the GCF of 9900 and 9905?

We will first find the prime factorization of 9900 and 9905. After we will calculate the factors of 9900 and 9905 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 9905

Prime factors of 9905 are 5, 7, 283. Prime factorization of 9905 in exponential form is:

9905 = 5¹ × 7¹ × 283¹

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 9905

List of positive integer factors of 9905 that divides 9900 without a remainder.

1, 5, 7, 35, 283, 1415, 1981

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9900 and 9905. The biggest common factor number is the GCF number.
So the greatest common factor 9900 and 9905 is 5.

Also check out the Least Common Multiple of 9900 and 9905