What is the Greatest Common Factor of 72912 and 72930?

Greatest common factor (GCF) of 72912 and 72930 is 6.

GCF(72912,72930) = 6

We will now calculate the prime factors of 72912 and 72930, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72912 and 72930.

How to find the GCF of 72912 and 72930?

We will first find the prime factorization of 72912 and 72930. After we will calculate the factors of 72912 and 72930 and find the biggest common factor number .

Step-1: Prime Factorization of 72912

Prime factors of 72912 are 2, 3, 7, 31. Prime factorization of 72912 in exponential form is:

72912 = 2⁴ × 3¹ × 7² × 31¹

Step-2: Prime Factorization of 72930

Prime factors of 72930 are 2, 3, 5, 11, 13, 17. Prime factorization of 72930 in exponential form is:

72930 = 2¹ × 3¹ × 5¹ × 11¹ × 13¹ × 17¹

Step-3: Factors of 72912

List of positive integer factors of 72912 that divides 72912 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 31, 42, 48, 49, 56, 62, 84, 93, 98, 112, 124, 147, 168, 186, 196, 217, 248, 294, 336, 372, 392, 434, 496, 588, 651, 744, 784, 868, 1176, 1302, 1488, 1519, 1736, 2352, 2604, 3038, 3472, 4557, 5208, 6076, 9114, 10416, 12152, 18228, 24304, 36456

Step-4: Factors of 72930

List of positive integer factors of 72930 that divides 72912 without a remainder.

1, 2, 3, 5, 6, 10, 11, 13, 15, 17, 22, 26, 30, 33, 34, 39, 51, 55, 65, 66, 78, 85, 102, 110, 130, 143, 165, 170, 187, 195, 221, 255, 286, 330, 374, 390, 429, 442, 510, 561, 663, 715, 858, 935, 1105, 1122, 1326, 1430, 1870, 2145, 2210, 2431, 2805, 3315, 4290, 4862, 5610, 6630, 7293, 12155, 14586, 24310, 36465

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72912 and 72930. The biggest common factor number is the GCF number.
So the greatest common factor 72912 and 72930 is 6.

Also check out the Least Common Multiple of 72912 and 72930