What is the Greatest Common Factor of 3570 and 3585?

Greatest common factor (GCF) of 3570 and 3585 is 15.

GCF(3570,3585) = 15

We will now calculate the prime factors of 3570 and 3585, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3570 and 3585.

How to find the GCF of 3570 and 3585?

We will first find the prime factorization of 3570 and 3585. After we will calculate the factors of 3570 and 3585 and find the biggest common factor number .

Step-1: Prime Factorization of 3570

Prime factors of 3570 are 2, 3, 5, 7, 17. Prime factorization of 3570 in exponential form is:

3570 = 2¹ × 3¹ × 5¹ × 7¹ × 17¹

Step-2: 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-3: Factors of 3570

List of positive integer factors of 3570 that divides 3570 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 17, 21, 30, 34, 35, 42, 51, 70, 85, 102, 105, 119, 170, 210, 238, 255, 357, 510, 595, 714, 1190, 1785

Step-4: Factors of 3585

List of positive integer factors of 3585 that divides 3570 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3570 and 3585. The biggest common factor number is the GCF number.
So the greatest common factor 3570 and 3585 is 15.

Also check out the Least Common Multiple of 3570 and 3585