What is the Greatest Common Factor of 75840 and 75856?

Greatest common factor (GCF) of 75840 and 75856 is 16.

GCF(75840,75856) = 16

We will now calculate the prime factors of 75840 and 75856, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75840 and 75856.

How to find the GCF of 75840 and 75856?

We will first find the prime factorization of 75840 and 75856. After we will calculate the factors of 75840 and 75856 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 75856

Prime factors of 75856 are 2, 11, 431. Prime factorization of 75856 in exponential form is:

75856 = 2⁴ × 11¹ × 431¹

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 75856

List of positive integer factors of 75856 that divides 75840 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 431, 862, 1724, 3448, 4741, 6896, 9482, 18964, 37928

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75840 and 75856. The biggest common factor number is the GCF number.
So the greatest common factor 75840 and 75856 is 16.

Also check out the Least Common Multiple of 75840 and 75856