What is the Greatest Common Factor of 3546 and 3564?

Greatest common factor (GCF) of 3546 and 3564 is 18.

GCF(3546,3564) = 18

We will now calculate the prime factors of 3546 and 3564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3546 and 3564.

How to find the GCF of 3546 and 3564?

We will first find the prime factorization of 3546 and 3564. After we will calculate the factors of 3546 and 3564 and find the biggest common factor number .

Step-1: Prime Factorization of 3546

Prime factors of 3546 are 2, 3, 197. Prime factorization of 3546 in exponential form is:

3546 = 2¹ × 3² × 197¹

Step-2: 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-3: Factors of 3546

List of positive integer factors of 3546 that divides 3546 without a remainder.

1, 2, 3, 6, 9, 18, 197, 394, 591, 1182, 1773

Step-4: Factors of 3564

List of positive integer factors of 3564 that divides 3546 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3546 and 3564. The biggest common factor number is the GCF number.
So the greatest common factor 3546 and 3564 is 18.

Also check out the Least Common Multiple of 3546 and 3564