What is the Greatest Common Factor of 9900 and 9912?

Greatest common factor (GCF) of 9900 and 9912 is 12.

GCF(9900,9912) = 12

We will now calculate the prime factors of 9900 and 9912, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9900 and 9912.

How to find the GCF of 9900 and 9912?

We will first find the prime factorization of 9900 and 9912. After we will calculate the factors of 9900 and 9912 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 9912

Prime factors of 9912 are 2, 3, 7, 59. Prime factorization of 9912 in exponential form is:

9912 = 2³ × 3¹ × 7¹ × 59¹

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 9912

List of positive integer factors of 9912 that divides 9900 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 59, 84, 118, 168, 177, 236, 354, 413, 472, 708, 826, 1239, 1416, 1652, 2478, 3304, 4956

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9900 and 9912. The biggest common factor number is the GCF number.
So the greatest common factor 9900 and 9912 is 12.

Also check out the Least Common Multiple of 9900 and 9912