What is the Greatest Common Factor of 17649 and 17667?

Greatest common factor (GCF) of 17649 and 17667 is 9.

GCF(17649,17667) = 9

We will now calculate the prime factors of 17649 and 17667, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17649 and 17667.

How to find the GCF of 17649 and 17667?

We will first find the prime factorization of 17649 and 17667. After we will calculate the factors of 17649 and 17667 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 17667

Prime factors of 17667 are 3, 13, 151. Prime factorization of 17667 in exponential form is:

17667 = 3² × 13¹ × 151¹

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 17667

List of positive integer factors of 17667 that divides 17649 without a remainder.

1, 3, 9, 13, 39, 117, 151, 453, 1359, 1963, 5889

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17649 and 17667. The biggest common factor number is the GCF number.
So the greatest common factor 17649 and 17667 is 9.

Also check out the Least Common Multiple of 17649 and 17667