What is the Greatest Common Factor of 39060 and 39072?

Greatest common factor (GCF) of 39060 and 39072 is 12.

GCF(39060,39072) = 12

We will now calculate the prime factors of 39060 and 39072, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39060 and 39072.

How to find the GCF of 39060 and 39072?

We will first find the prime factorization of 39060 and 39072. After we will calculate the factors of 39060 and 39072 and find the biggest common factor number .

Step-1: Prime Factorization of 39060

Prime factors of 39060 are 2, 3, 5, 7, 31. Prime factorization of 39060 in exponential form is:

39060 = 2² × 3² × 5¹ × 7¹ × 31¹

Step-2: Prime Factorization of 39072

Prime factors of 39072 are 2, 3, 11, 37. Prime factorization of 39072 in exponential form is:

39072 = 2⁵ × 3¹ × 11¹ × 37¹

Step-3: Factors of 39060

List of positive integer factors of 39060 that divides 39060 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 31, 35, 36, 42, 45, 60, 62, 63, 70, 84, 90, 93, 105, 124, 126, 140, 155, 180, 186, 210, 217, 252, 279, 310, 315, 372, 420, 434, 465, 558, 620, 630, 651, 868, 930, 1085, 1116, 1260, 1302, 1395, 1860, 1953, 2170, 2604, 2790, 3255, 3906, 4340, 5580, 6510, 7812, 9765, 13020, 19530

Step-4: Factors of 39072

List of positive integer factors of 39072 that divides 39060 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 37, 44, 48, 66, 74, 88, 96, 111, 132, 148, 176, 222, 264, 296, 352, 407, 444, 528, 592, 814, 888, 1056, 1184, 1221, 1628, 1776, 2442, 3256, 3552, 4884, 6512, 9768, 13024, 19536

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39060 and 39072. The biggest common factor number is the GCF number.
So the greatest common factor 39060 and 39072 is 12.

Also check out the Least Common Multiple of 39060 and 39072