What is the Greatest Common Factor of 73710 and 73728?

Greatest common factor (GCF) of 73710 and 73728 is 18.

GCF(73710,73728) = 18

We will now calculate the prime factors of 73710 and 73728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73710 and 73728.

How to find the GCF of 73710 and 73728?

We will first find the prime factorization of 73710 and 73728. After we will calculate the factors of 73710 and 73728 and find the biggest common factor number .

Step-1: Prime Factorization of 73710

Prime factors of 73710 are 2, 3, 5, 7, 13. Prime factorization of 73710 in exponential form is:

73710 = 2¹ × 3⁴ × 5¹ × 7¹ × 13¹

Step-2: Prime Factorization of 73728

Prime factors of 73728 are 2, 3. Prime factorization of 73728 in exponential form is:

73728 = 2¹³ × 3²

Step-3: Factors of 73710

List of positive integer factors of 73710 that divides 73710 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 13, 14, 15, 18, 21, 26, 27, 30, 35, 39, 42, 45, 54, 63, 65, 70, 78, 81, 90, 91, 105, 117, 126, 130, 135, 162, 182, 189, 195, 210, 234, 270, 273, 315, 351, 378, 390, 405, 455, 546, 567, 585, 630, 702, 810, 819, 910, 945, 1053, 1134, 1170, 1365, 1638, 1755, 1890, 2106, 2457, 2730, 2835, 3510, 4095, 4914, 5265, 5670, 7371, 8190, 10530, 12285, 14742, 24570, 36855

Step-4: Factors of 73728

List of positive integer factors of 73728 that divides 73710 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2048, 2304, 3072, 4096, 4608, 6144, 8192, 9216, 12288, 18432, 24576, 36864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73710 and 73728. The biggest common factor number is the GCF number.
So the greatest common factor 73710 and 73728 is 18.

Also check out the Least Common Multiple of 73710 and 73728