What is the Greatest Common Factor of 33660 and 33675?

Greatest common factor (GCF) of 33660 and 33675 is 15.

GCF(33660,33675) = 15

We will now calculate the prime factors of 33660 and 33675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33660 and 33675.

How to find the GCF of 33660 and 33675?

We will first find the prime factorization of 33660 and 33675. After we will calculate the factors of 33660 and 33675 and find the biggest common factor number .

Step-1: Prime Factorization of 33660

Prime factors of 33660 are 2, 3, 5, 11, 17. Prime factorization of 33660 in exponential form is:

33660 = 2² × 3² × 5¹ × 11¹ × 17¹

Step-2: Prime Factorization of 33675

Prime factors of 33675 are 3, 5, 449. Prime factorization of 33675 in exponential form is:

33675 = 3¹ × 5² × 449¹

Step-3: Factors of 33660

List of positive integer factors of 33660 that divides 33660 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 17, 18, 20, 22, 30, 33, 34, 36, 44, 45, 51, 55, 60, 66, 68, 85, 90, 99, 102, 110, 132, 153, 165, 170, 180, 187, 198, 204, 220, 255, 306, 330, 340, 374, 396, 495, 510, 561, 612, 660, 748, 765, 935, 990, 1020, 1122, 1530, 1683, 1870, 1980, 2244, 2805, 3060, 3366, 3740, 5610, 6732, 8415, 11220, 16830

Step-4: Factors of 33675

List of positive integer factors of 33675 that divides 33660 without a remainder.

1, 3, 5, 15, 25, 75, 449, 1347, 2245, 6735, 11225

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33660 and 33675. The biggest common factor number is the GCF number.
So the greatest common factor 33660 and 33675 is 15.

Also check out the Least Common Multiple of 33660 and 33675