What is the Greatest Common Factor of 75856 and 75872?

Greatest common factor (GCF) of 75856 and 75872 is 16.

GCF(75856,75872) = 16

We will now calculate the prime factors of 75856 and 75872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75856 and 75872.

How to find the GCF of 75856 and 75872?

We will first find the prime factorization of 75856 and 75872. After we will calculate the factors of 75856 and 75872 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75872

Prime factors of 75872 are 2, 2371. Prime factorization of 75872 in exponential form is:

75872 = 2⁵ × 2371¹

Step-3: Factors of 75856

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

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

Step-4: Factors of 75872

List of positive integer factors of 75872 that divides 75856 without a remainder.

1, 2, 4, 8, 16, 32, 2371, 4742, 9484, 18968, 37936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75856 and 75872. The biggest common factor number is the GCF number.
So the greatest common factor 75856 and 75872 is 16.

Also check out the Least Common Multiple of 75856 and 75872