What is the Greatest Common Factor of 51288 and 51300?

Greatest common factor (GCF) of 51288 and 51300 is 12.

GCF(51288,51300) = 12

We will now calculate the prime factors of 51288 and 51300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51288 and 51300.

How to find the GCF of 51288 and 51300?

We will first find the prime factorization of 51288 and 51300. After we will calculate the factors of 51288 and 51300 and find the biggest common factor number .

Step-1: Prime Factorization of 51288

Prime factors of 51288 are 2, 3, 2137. Prime factorization of 51288 in exponential form is:

51288 = 2³ × 3¹ × 2137¹

Step-2: 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-3: Factors of 51288

List of positive integer factors of 51288 that divides 51288 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 2137, 4274, 6411, 8548, 12822, 17096, 25644

Step-4: Factors of 51300

List of positive integer factors of 51300 that divides 51288 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51288 and 51300. The biggest common factor number is the GCF number.
So the greatest common factor 51288 and 51300 is 12.

Also check out the Least Common Multiple of 51288 and 51300