What is the Greatest Common Factor of 9888 and 9900?

Greatest common factor (GCF) of 9888 and 9900 is 12.

GCF(9888,9900) = 12

We will now calculate the prime factors of 9888 and 9900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9888 and 9900.

How to find the GCF of 9888 and 9900?

We will first find the prime factorization of 9888 and 9900. After we will calculate the factors of 9888 and 9900 and find the biggest common factor number .

Step-1: Prime Factorization of 9888

Prime factors of 9888 are 2, 3, 103. Prime factorization of 9888 in exponential form is:

9888 = 2⁵ × 3¹ × 103¹

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 9888

List of positive integer factors of 9888 that divides 9888 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 103, 206, 309, 412, 618, 824, 1236, 1648, 2472, 3296, 4944

Step-4: Factors of 9900

List of positive integer factors of 9900 that divides 9888 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 9888 and 9900. The biggest common factor number is the GCF number.
So the greatest common factor 9888 and 9900 is 12.

Also check out the Least Common Multiple of 9888 and 9900