What is the Greatest Common Factor of 51600 and 51609?

Greatest common factor (GCF) of 51600 and 51609 is 3.

GCF(51600,51609) = 3

We will now calculate the prime factors of 51600 and 51609, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51600 and 51609.

How to find the GCF of 51600 and 51609?

We will first find the prime factorization of 51600 and 51609. After we will calculate the factors of 51600 and 51609 and find the biggest common factor number .

Step-1: Prime Factorization of 51600

Prime factors of 51600 are 2, 3, 5, 43. Prime factorization of 51600 in exponential form is:

51600 = 2⁴ × 3¹ × 5² × 43¹

Step-2: Prime Factorization of 51609

Prime factors of 51609 are 3, 17203. Prime factorization of 51609 in exponential form is:

51609 = 3¹ × 17203¹

Step-3: Factors of 51600

List of positive integer factors of 51600 that divides 51600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 43, 48, 50, 60, 75, 80, 86, 100, 120, 129, 150, 172, 200, 215, 240, 258, 300, 344, 400, 430, 516, 600, 645, 688, 860, 1032, 1075, 1200, 1290, 1720, 2064, 2150, 2580, 3225, 3440, 4300, 5160, 6450, 8600, 10320, 12900, 17200, 25800

Step-4: Factors of 51609

List of positive integer factors of 51609 that divides 51600 without a remainder.

1, 3, 17203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51600 and 51609. The biggest common factor number is the GCF number.
So the greatest common factor 51600 and 51609 is 3.

Also check out the Least Common Multiple of 51600 and 51609