What is the Greatest Common Factor of 75546 and 75564?

Greatest common factor (GCF) of 75546 and 75564 is 18.

GCF(75546,75564) = 18

We will now calculate the prime factors of 75546 and 75564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75546 and 75564.

How to find the GCF of 75546 and 75564?

We will first find the prime factorization of 75546 and 75564. After we will calculate the factors of 75546 and 75564 and find the biggest common factor number .

Step-1: Prime Factorization of 75546

Prime factors of 75546 are 2, 3, 1399. Prime factorization of 75546 in exponential form is:

75546 = 2¹ × 3³ × 1399¹

Step-2: Prime Factorization of 75564

Prime factors of 75564 are 2, 3, 2099. Prime factorization of 75564 in exponential form is:

75564 = 2² × 3² × 2099¹

Step-3: Factors of 75546

List of positive integer factors of 75546 that divides 75546 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 1399, 2798, 4197, 8394, 12591, 25182, 37773

Step-4: Factors of 75564

List of positive integer factors of 75564 that divides 75546 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 2099, 4198, 6297, 8396, 12594, 18891, 25188, 37782

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75546 and 75564. The biggest common factor number is the GCF number.
So the greatest common factor 75546 and 75564 is 18.

Also check out the Least Common Multiple of 75546 and 75564