What is the Greatest Common Factor of 75840 and 75852?

Greatest common factor (GCF) of 75840 and 75852 is 12.

GCF(75840,75852) = 12

We will now calculate the prime factors of 75840 and 75852, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75840 and 75852.

How to find the GCF of 75840 and 75852?

We will first find the prime factorization of 75840 and 75852. After we will calculate the factors of 75840 and 75852 and find the biggest common factor number .

Step-1: Prime Factorization of 75840

Prime factors of 75840 are 2, 3, 5, 79. Prime factorization of 75840 in exponential form is:

75840 = 2⁶ × 3¹ × 5¹ × 79¹

Step-2: Prime Factorization of 75852

Prime factors of 75852 are 2, 3, 7, 43. Prime factorization of 75852 in exponential form is:

75852 = 2² × 3² × 7² × 43¹

Step-3: Factors of 75840

List of positive integer factors of 75840 that divides 75840 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 79, 80, 96, 120, 158, 160, 192, 237, 240, 316, 320, 395, 474, 480, 632, 790, 948, 960, 1185, 1264, 1580, 1896, 2370, 2528, 3160, 3792, 4740, 5056, 6320, 7584, 9480, 12640, 15168, 18960, 25280, 37920

Step-4: Factors of 75852

List of positive integer factors of 75852 that divides 75840 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 43, 49, 63, 84, 86, 98, 126, 129, 147, 172, 196, 252, 258, 294, 301, 387, 441, 516, 588, 602, 774, 882, 903, 1204, 1548, 1764, 1806, 2107, 2709, 3612, 4214, 5418, 6321, 8428, 10836, 12642, 18963, 25284, 37926

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75840 and 75852. The biggest common factor number is the GCF number.
So the greatest common factor 75840 and 75852 is 12.

Also check out the Least Common Multiple of 75840 and 75852