What is the Greatest Common Factor of 75708 and 75728?

Greatest common factor (GCF) of 75708 and 75728 is 4.

GCF(75708,75728) = 4

We will now calculate the prime factors of 75708 and 75728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75708 and 75728.

How to find the GCF of 75708 and 75728?

We will first find the prime factorization of 75708 and 75728. After we will calculate the factors of 75708 and 75728 and find the biggest common factor number .

Step-1: Prime Factorization of 75708

Prime factors of 75708 are 2, 3, 701. Prime factorization of 75708 in exponential form is:

75708 = 2² × 3³ × 701¹

Step-2: Prime Factorization of 75728

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

75728 = 2⁴ × 4733¹

Step-3: Factors of 75708

List of positive integer factors of 75708 that divides 75708 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 701, 1402, 2103, 2804, 4206, 6309, 8412, 12618, 18927, 25236, 37854

Step-4: Factors of 75728

List of positive integer factors of 75728 that divides 75708 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75708 and 75728. The biggest common factor number is the GCF number.
So the greatest common factor 75708 and 75728 is 4.

Also check out the Least Common Multiple of 75708 and 75728