What is the Greatest Common Factor of 3540 and 3549?

Greatest common factor (GCF) of 3540 and 3549 is 3.

GCF(3540,3549) = 3

We will now calculate the prime factors of 3540 and 3549, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3540 and 3549.

How to find the GCF of 3540 and 3549?

We will first find the prime factorization of 3540 and 3549. After we will calculate the factors of 3540 and 3549 and find the biggest common factor number .

Step-1: Prime Factorization of 3540

Prime factors of 3540 are 2, 3, 5, 59. Prime factorization of 3540 in exponential form is:

3540 = 2² × 3¹ × 5¹ × 59¹

Step-2: Prime Factorization of 3549

Prime factors of 3549 are 3, 7, 13. Prime factorization of 3549 in exponential form is:

3549 = 3¹ × 7¹ × 13²

Step-3: Factors of 3540

List of positive integer factors of 3540 that divides 3540 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 59, 60, 118, 177, 236, 295, 354, 590, 708, 885, 1180, 1770

Step-4: Factors of 3549

List of positive integer factors of 3549 that divides 3540 without a remainder.

1, 3, 7, 13, 21, 39, 91, 169, 273, 507, 1183

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3540 and 3549. The biggest common factor number is the GCF number.
So the greatest common factor 3540 and 3549 is 3.

Also check out the Least Common Multiple of 3540 and 3549