What is the Greatest Common Factor of 73200 and 73216?

Greatest common factor (GCF) of 73200 and 73216 is 16.

GCF(73200,73216) = 16

We will now calculate the prime factors of 73200 and 73216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73200 and 73216.

How to find the GCF of 73200 and 73216?

We will first find the prime factorization of 73200 and 73216. After we will calculate the factors of 73200 and 73216 and find the biggest common factor number .

Step-1: Prime Factorization of 73200

Prime factors of 73200 are 2, 3, 5, 61. Prime factorization of 73200 in exponential form is:

73200 = 2⁴ × 3¹ × 5² × 61¹

Step-2: Prime Factorization of 73216

Prime factors of 73216 are 2, 11, 13. Prime factorization of 73216 in exponential form is:

73216 = 2⁹ × 11¹ × 13¹

Step-3: Factors of 73200

List of positive integer factors of 73200 that divides 73200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 61, 75, 80, 100, 120, 122, 150, 183, 200, 240, 244, 300, 305, 366, 400, 488, 600, 610, 732, 915, 976, 1200, 1220, 1464, 1525, 1830, 2440, 2928, 3050, 3660, 4575, 4880, 6100, 7320, 9150, 12200, 14640, 18300, 24400, 36600

Step-4: Factors of 73216

List of positive integer factors of 73216 that divides 73200 without a remainder.

1, 2, 4, 8, 11, 13, 16, 22, 26, 32, 44, 52, 64, 88, 104, 128, 143, 176, 208, 256, 286, 352, 416, 512, 572, 704, 832, 1144, 1408, 1664, 2288, 2816, 3328, 4576, 5632, 6656, 9152, 18304, 36608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73200 and 73216. The biggest common factor number is the GCF number.
So the greatest common factor 73200 and 73216 is 16.

Also check out the Least Common Multiple of 73200 and 73216