What is the Greatest Common Factor of 75728 and 75734?

Greatest common factor (GCF) of 75728 and 75734 is 2.

GCF(75728,75734) = 2

We will now calculate the prime factors of 75728 and 75734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75728 and 75734.

How to find the GCF of 75728 and 75734?

We will first find the prime factorization of 75728 and 75734. After we will calculate the factors of 75728 and 75734 and find the biggest common factor number .

Step-1: Prime Factorization of 75728

Prime factors of 75728 are 2, 4733. Prime factorization of 75728 in exponential form is:

75728 = 2⁴ × 4733¹

Step-2: Prime Factorization of 75734

Prime factors of 75734 are 2, 19, 1993. Prime factorization of 75734 in exponential form is:

75734 = 2¹ × 19¹ × 1993¹

Step-3: Factors of 75728

List of positive integer factors of 75728 that divides 75728 without a remainder.

1, 2, 4, 8, 16, 4733, 9466, 18932, 37864

Step-4: Factors of 75734

List of positive integer factors of 75734 that divides 75728 without a remainder.

1, 2, 19, 38, 1993, 3986, 37867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75728 and 75734. The biggest common factor number is the GCF number.
So the greatest common factor 75728 and 75734 is 2.

Also check out the Least Common Multiple of 75728 and 75734