What is the Greatest Common Factor of 17649 and 17658?

Greatest common factor (GCF) of 17649 and 17658 is 9.

GCF(17649,17658) = 9

We will now calculate the prime factors of 17649 and 17658, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17649 and 17658.

How to find the GCF of 17649 and 17658?

We will first find the prime factorization of 17649 and 17658. After we will calculate the factors of 17649 and 17658 and find the biggest common factor number .

Step-1: Prime Factorization of 17649

Prime factors of 17649 are 3, 37, 53. Prime factorization of 17649 in exponential form is:

17649 = 3² × 37¹ × 53¹

Step-2: Prime Factorization of 17658

Prime factors of 17658 are 2, 3, 109. Prime factorization of 17658 in exponential form is:

17658 = 2¹ × 3⁴ × 109¹

Step-3: Factors of 17649

List of positive integer factors of 17649 that divides 17649 without a remainder.

1, 3, 9, 37, 53, 111, 159, 333, 477, 1961, 5883

Step-4: Factors of 17658

List of positive integer factors of 17658 that divides 17649 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 109, 162, 218, 327, 654, 981, 1962, 2943, 5886, 8829

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17649 and 17658. The biggest common factor number is the GCF number.
So the greatest common factor 17649 and 17658 is 9.

Also check out the Least Common Multiple of 17649 and 17658