What is the Greatest Common Factor of 51300 and 51319?

Greatest common factor (GCF) of 51300 and 51319 is 19.

GCF(51300,51319) = 19

We will now calculate the prime factors of 51300 and 51319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51300 and 51319.

How to find the GCF of 51300 and 51319?

We will first find the prime factorization of 51300 and 51319. After we will calculate the factors of 51300 and 51319 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 51319

Prime factors of 51319 are 19, 37, 73. Prime factorization of 51319 in exponential form is:

51319 = 19¹ × 37¹ × 73¹

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 51319

List of positive integer factors of 51319 that divides 51300 without a remainder.

1, 19, 37, 73, 703, 1387, 2701

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51300 and 51319. The biggest common factor number is the GCF number.
So the greatest common factor 51300 and 51319 is 19.

Also check out the Least Common Multiple of 51300 and 51319