What is the Greatest Common Factor of 99200 and 99216?

Greatest common factor (GCF) of 99200 and 99216 is 16.

GCF(99200,99216) = 16

We will now calculate the prime factors of 99200 and 99216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 99200 and 99216.

How to find the GCF of 99200 and 99216?

We will first find the prime factorization of 99200 and 99216. After we will calculate the factors of 99200 and 99216 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 99216

Prime factors of 99216 are 2, 3, 13, 53. Prime factorization of 99216 in exponential form is:

99216 = 2⁴ × 3² × 13¹ × 53¹

Step-3: Factors of 99200

List of positive integer factors of 99200 that divides 99200 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

Step-4: Factors of 99216

List of positive integer factors of 99216 that divides 99200 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 53, 72, 78, 104, 106, 117, 144, 156, 159, 208, 212, 234, 312, 318, 424, 468, 477, 624, 636, 689, 848, 936, 954, 1272, 1378, 1872, 1908, 2067, 2544, 2756, 3816, 4134, 5512, 6201, 7632, 8268, 11024, 12402, 16536, 24804, 33072, 49608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 99200 and 99216. The biggest common factor number is the GCF number.
So the greatest common factor 99200 and 99216 is 16.

Also check out the Least Common Multiple of 99200 and 99216