What is the Greatest Common Factor of 51300 and 51315?

Greatest common factor (GCF) of 51300 and 51315 is 15.

GCF(51300,51315) = 15

We will now calculate the prime factors of 51300 and 51315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51300 and 51315.

How to find the GCF of 51300 and 51315?

We will first find the prime factorization of 51300 and 51315. After we will calculate the factors of 51300 and 51315 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 51315

Prime factors of 51315 are 3, 5, 11, 311. Prime factorization of 51315 in exponential form is:

51315 = 3¹ × 5¹ × 11¹ × 311¹

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 51315

List of positive integer factors of 51315 that divides 51300 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 311, 933, 1555, 3421, 4665, 10263, 17105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51300 and 51315. The biggest common factor number is the GCF number.
So the greatest common factor 51300 and 51315 is 15.

Also check out the Least Common Multiple of 51300 and 51315