What is the Greatest Common Factor of 99180 and 99200?

Greatest common factor (GCF) of 99180 and 99200 is 20.

GCF(99180,99200) = 20

We will now calculate the prime factors of 99180 and 99200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 99180 and 99200.

How to find the GCF of 99180 and 99200?

We will first find the prime factorization of 99180 and 99200. After we will calculate the factors of 99180 and 99200 and find the biggest common factor number .

Step-1: Prime Factorization of 99180

Prime factors of 99180 are 2, 3, 5, 19, 29. Prime factorization of 99180 in exponential form is:

99180 = 2² × 3² × 5¹ × 19¹ × 29¹

Step-2: Prime Factorization of 99200

Prime factors of 99200 are 2, 5, 31. Prime factorization of 99200 in exponential form is:

99200 = 2⁷ × 5² × 31¹

Step-3: Factors of 99180

List of positive integer factors of 99180 that divides 99180 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 29, 30, 36, 38, 45, 57, 58, 60, 76, 87, 90, 95, 114, 116, 145, 171, 174, 180, 190, 228, 261, 285, 290, 342, 348, 380, 435, 522, 551, 570, 580, 684, 855, 870, 1044, 1102, 1140, 1305, 1653, 1710, 1740, 2204, 2610, 2755, 3306, 3420, 4959, 5220, 5510, 6612, 8265, 9918, 11020, 16530, 19836, 24795, 33060, 49590

Step-4: Factors of 99200

List of positive integer factors of 99200 that divides 99180 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 31, 32, 40, 50, 62, 64, 80, 100, 124, 128, 155, 160, 200, 248, 310, 320, 400, 496, 620, 640, 775, 800, 992, 1240, 1550, 1600, 1984, 2480, 3100, 3200, 3968, 4960, 6200, 9920, 12400, 19840, 24800, 49600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 99180 and 99200. The biggest common factor number is the GCF number.
So the greatest common factor 99180 and 99200 is 20.

Also check out the Least Common Multiple of 99180 and 99200