What is the Greatest Common Factor of 17640 and 17649?

Greatest common factor (GCF) of 17640 and 17649 is 9.

GCF(17640,17649) = 9

We will now calculate the prime factors of 17640 and 17649, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17640 and 17649.

How to find the GCF of 17640 and 17649?

We will first find the prime factorization of 17640 and 17649. After we will calculate the factors of 17640 and 17649 and find the biggest common factor number .

Step-1: Prime Factorization of 17640

Prime factors of 17640 are 2, 3, 5, 7. Prime factorization of 17640 in exponential form is:

17640 = 2³ × 3² × 5¹ × 7²

Step-2: 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-3: Factors of 17640

List of positive integer factors of 17640 that divides 17640 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 49, 56, 60, 63, 70, 72, 84, 90, 98, 105, 120, 126, 140, 147, 168, 180, 196, 210, 245, 252, 280, 294, 315, 360, 392, 420, 441, 490, 504, 588, 630, 735, 840, 882, 980, 1176, 1260, 1470, 1764, 1960, 2205, 2520, 2940, 3528, 4410, 5880, 8820

Step-4: Factors of 17649

List of positive integer factors of 17649 that divides 17640 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17640 and 17649. The biggest common factor number is the GCF number.
So the greatest common factor 17640 and 17649 is 9.

Also check out the Least Common Multiple of 17640 and 17649