What is the Greatest Common Factor of 30585 and 30600?

Greatest common factor (GCF) of 30585 and 30600 is 15.

GCF(30585,30600) = 15

We will now calculate the prime factors of 30585 and 30600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30585 and 30600.

How to find the GCF of 30585 and 30600?

We will first find the prime factorization of 30585 and 30600. After we will calculate the factors of 30585 and 30600 and find the biggest common factor number .

Step-1: Prime Factorization of 30585

Prime factors of 30585 are 3, 5, 2039. Prime factorization of 30585 in exponential form is:

30585 = 3¹ × 5¹ × 2039¹

Step-2: Prime Factorization of 30600

Prime factors of 30600 are 2, 3, 5, 17. Prime factorization of 30600 in exponential form is:

30600 = 2³ × 3² × 5² × 17¹

Step-3: Factors of 30585

List of positive integer factors of 30585 that divides 30585 without a remainder.

1, 3, 5, 15, 2039, 6117, 10195

Step-4: Factors of 30600

List of positive integer factors of 30600 that divides 30585 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 17, 18, 20, 24, 25, 30, 34, 36, 40, 45, 50, 51, 60, 68, 72, 75, 85, 90, 100, 102, 120, 136, 150, 153, 170, 180, 200, 204, 225, 255, 300, 306, 340, 360, 408, 425, 450, 510, 600, 612, 680, 765, 850, 900, 1020, 1224, 1275, 1530, 1700, 1800, 2040, 2550, 3060, 3400, 3825, 5100, 6120, 7650, 10200, 15300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30585 and 30600. The biggest common factor number is the GCF number.
So the greatest common factor 30585 and 30600 is 15.

Also check out the Least Common Multiple of 30585 and 30600