What is the Greatest Common Factor of 51280 and 51300?

Greatest common factor (GCF) of 51280 and 51300 is 20.

GCF(51280,51300) = 20

We will now calculate the prime factors of 51280 and 51300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51280 and 51300.

How to find the GCF of 51280 and 51300?

We will first find the prime factorization of 51280 and 51300. After we will calculate the factors of 51280 and 51300 and find the biggest common factor number .

Step-1: Prime Factorization of 51280

Prime factors of 51280 are 2, 5, 641. Prime factorization of 51280 in exponential form is:

51280 = 2⁴ × 5¹ × 641¹

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 51280

List of positive integer factors of 51280 that divides 51280 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 641, 1282, 2564, 3205, 5128, 6410, 10256, 12820, 25640

Step-4: Factors of 51300

List of positive integer factors of 51300 that divides 51280 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 51280 and 51300. The biggest common factor number is the GCF number.
So the greatest common factor 51280 and 51300 is 20.

Also check out the Least Common Multiple of 51280 and 51300