What is the Greatest Common Factor of 39600 and 39609?

Greatest common factor (GCF) of 39600 and 39609 is 9.

GCF(39600,39609) = 9

We will now calculate the prime factors of 39600 and 39609, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39600 and 39609.

How to find the GCF of 39600 and 39609?

We will first find the prime factorization of 39600 and 39609. After we will calculate the factors of 39600 and 39609 and find the biggest common factor number .

Step-1: Prime Factorization of 39600

Prime factors of 39600 are 2, 3, 5, 11. Prime factorization of 39600 in exponential form is:

39600 = 2⁴ × 3² × 5² × 11¹

Step-2: Prime Factorization of 39609

Prime factors of 39609 are 3, 163. Prime factorization of 39609 in exponential form is:

39609 = 3⁵ × 163¹

Step-3: Factors of 39600

List of positive integer factors of 39600 that divides 39600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 25, 30, 33, 36, 40, 44, 45, 48, 50, 55, 60, 66, 72, 75, 80, 88, 90, 99, 100, 110, 120, 132, 144, 150, 165, 176, 180, 198, 200, 220, 225, 240, 264, 275, 300, 330, 360, 396, 400, 440, 450, 495, 528, 550, 600, 660, 720, 792, 825, 880, 900, 990, 1100, 1200, 1320, 1584, 1650, 1800, 1980, 2200, 2475, 2640, 3300, 3600, 3960, 4400, 4950, 6600, 7920, 9900, 13200, 19800

Step-4: Factors of 39609

List of positive integer factors of 39609 that divides 39600 without a remainder.

1, 3, 9, 27, 81, 163, 243, 489, 1467, 4401, 13203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39600 and 39609. The biggest common factor number is the GCF number.
So the greatest common factor 39600 and 39609 is 9.

Also check out the Least Common Multiple of 39600 and 39609