What is the Greatest Common Factor of 75969 and 75984?

Greatest common factor (GCF) of 75969 and 75984 is 3.

GCF(75969,75984) = 3

We will now calculate the prime factors of 75969 and 75984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75969 and 75984.

How to find the GCF of 75969 and 75984?

We will first find the prime factorization of 75969 and 75984. After we will calculate the factors of 75969 and 75984 and find the biggest common factor number .

Step-1: Prime Factorization of 75969

Prime factors of 75969 are 3, 23, 367. Prime factorization of 75969 in exponential form is:

75969 = 3² × 23¹ × 367¹

Step-2: Prime Factorization of 75984

Prime factors of 75984 are 2, 3, 1583. Prime factorization of 75984 in exponential form is:

75984 = 2⁴ × 3¹ × 1583¹

Step-3: Factors of 75969

List of positive integer factors of 75969 that divides 75969 without a remainder.

1, 3, 9, 23, 69, 207, 367, 1101, 3303, 8441, 25323

Step-4: Factors of 75984

List of positive integer factors of 75984 that divides 75969 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1583, 3166, 4749, 6332, 9498, 12664, 18996, 25328, 37992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75969 and 75984. The biggest common factor number is the GCF number.
So the greatest common factor 75969 and 75984 is 3.

Also check out the Least Common Multiple of 75969 and 75984