What is the Greatest Common Factor of 3564 and 3570?

Greatest common factor (GCF) of 3564 and 3570 is 6.

GCF(3564,3570) = 6

We will now calculate the prime factors of 3564 and 3570, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3564 and 3570.

How to find the GCF of 3564 and 3570?

We will first find the prime factorization of 3564 and 3570. After we will calculate the factors of 3564 and 3570 and find the biggest common factor number .

Step-1: Prime Factorization of 3564

Prime factors of 3564 are 2, 3, 11. Prime factorization of 3564 in exponential form is:

3564 = 2² × 3⁴ × 11¹

Step-2: 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-3: Factors of 3564

List of positive integer factors of 3564 that divides 3564 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 81, 99, 108, 132, 162, 198, 297, 324, 396, 594, 891, 1188, 1782

Step-4: Factors of 3570

List of positive integer factors of 3570 that divides 3564 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3564 and 3570. The biggest common factor number is the GCF number.
So the greatest common factor 3564 and 3570 is 6.

Also check out the Least Common Multiple of 3564 and 3570