What is the Greatest Common Factor of 3585 and 3600?

Greatest common factor (GCF) of 3585 and 3600 is 15.

GCF(3585,3600) = 15

We will now calculate the prime factors of 3585 and 3600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3585 and 3600.

How to find the GCF of 3585 and 3600?

We will first find the prime factorization of 3585 and 3600. After we will calculate the factors of 3585 and 3600 and find the biggest common factor number .

Step-1: Prime Factorization of 3585

Prime factors of 3585 are 3, 5, 239. Prime factorization of 3585 in exponential form is:

3585 = 3¹ × 5¹ × 239¹

Step-2: Prime Factorization of 3600

Prime factors of 3600 are 2, 3, 5. Prime factorization of 3600 in exponential form is:

3600 = 2⁴ × 3² × 5²

Step-3: Factors of 3585

List of positive integer factors of 3585 that divides 3585 without a remainder.

1, 3, 5, 15, 239, 717, 1195

Step-4: Factors of 3600

List of positive integer factors of 3600 that divides 3585 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3585 and 3600. The biggest common factor number is the GCF number.
So the greatest common factor 3585 and 3600 is 15.

Also check out the Least Common Multiple of 3585 and 3600