What is the Greatest Common Factor of 51300 and 51309?

Greatest common factor (GCF) of 51300 and 51309 is 9.

GCF(51300,51309) = 9

We will now calculate the prime factors of 51300 and 51309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51300 and 51309.

How to find the GCF of 51300 and 51309?

We will first find the prime factorization of 51300 and 51309. After we will calculate the factors of 51300 and 51309 and find the biggest common factor number .

Step-1: Prime Factorization of 51300

Prime factors of 51300 are 2, 3, 5, 19. Prime factorization of 51300 in exponential form is:

51300 = 2² × 3³ × 5² × 19¹

Step-2: Prime Factorization of 51309

Prime factors of 51309 are 3, 5701. Prime factorization of 51309 in exponential form is:

51309 = 3² × 5701¹

Step-3: Factors of 51300

List of positive integer factors of 51300 that divides 51300 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 27, 30, 36, 38, 45, 50, 54, 57, 60, 75, 76, 90, 95, 100, 108, 114, 135, 150, 171, 180, 190, 225, 228, 270, 285, 300, 342, 380, 450, 475, 513, 540, 570, 675, 684, 855, 900, 950, 1026, 1140, 1350, 1425, 1710, 1900, 2052, 2565, 2700, 2850, 3420, 4275, 5130, 5700, 8550, 10260, 12825, 17100, 25650

Step-4: Factors of 51309

List of positive integer factors of 51309 that divides 51300 without a remainder.

1, 3, 9, 5701, 17103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51300 and 51309. The biggest common factor number is the GCF number.
So the greatest common factor 51300 and 51309 is 9.

Also check out the Least Common Multiple of 51300 and 51309