What is the Greatest Common Factor of 9891 and 9900?

Greatest common factor (GCF) of 9891 and 9900 is 9.

GCF(9891,9900) = 9

We will now calculate the prime factors of 9891 and 9900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9891 and 9900.

How to find the GCF of 9891 and 9900?

We will first find the prime factorization of 9891 and 9900. After we will calculate the factors of 9891 and 9900 and find the biggest common factor number .

Step-1: Prime Factorization of 9891

Prime factors of 9891 are 3, 7, 157. Prime factorization of 9891 in exponential form is:

9891 = 3² × 7¹ × 157¹

Step-2: 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-3: Factors of 9891

List of positive integer factors of 9891 that divides 9891 without a remainder.

1, 3, 7, 9, 21, 63, 157, 471, 1099, 1413, 3297

Step-4: Factors of 9900

List of positive integer factors of 9900 that divides 9891 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9891 and 9900. The biggest common factor number is the GCF number.
So the greatest common factor 9891 and 9900 is 9.

Also check out the Least Common Multiple of 9891 and 9900