What is the Greatest Common Factor of 51300 and 51305?

Greatest common factor (GCF) of 51300 and 51305 is 5.

GCF(51300,51305) = 5

We will now calculate the prime factors of 51300 and 51305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51300 and 51305.

How to find the GCF of 51300 and 51305?

We will first find the prime factorization of 51300 and 51305. After we will calculate the factors of 51300 and 51305 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 51305

Prime factors of 51305 are 5, 31, 331. Prime factorization of 51305 in exponential form is:

51305 = 5¹ × 31¹ × 331¹

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 51305

List of positive integer factors of 51305 that divides 51300 without a remainder.

1, 5, 31, 155, 331, 1655, 10261

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51300 and 51305. The biggest common factor number is the GCF number.
So the greatest common factor 51300 and 51305 is 5.

Also check out the Least Common Multiple of 51300 and 51305