What is the Greatest Common Factor of 75564 and 75570?

Greatest common factor (GCF) of 75564 and 75570 is 6.

GCF(75564,75570) = 6

We will now calculate the prime factors of 75564 and 75570, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75564 and 75570.

How to find the GCF of 75564 and 75570?

We will first find the prime factorization of 75564 and 75570. After we will calculate the factors of 75564 and 75570 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75570

Prime factors of 75570 are 2, 3, 5, 11, 229. Prime factorization of 75570 in exponential form is:

75570 = 2¹ × 3¹ × 5¹ × 11¹ × 229¹

Step-3: Factors of 75564

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

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

Step-4: Factors of 75570

List of positive integer factors of 75570 that divides 75564 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 229, 330, 458, 687, 1145, 1374, 2290, 2519, 3435, 5038, 6870, 7557, 12595, 15114, 25190, 37785

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75564 and 75570. The biggest common factor number is the GCF number.
So the greatest common factor 75564 and 75570 is 6.

Also check out the Least Common Multiple of 75564 and 75570