What is the Greatest Common Factor of 51400 and 51405?

Greatest common factor (GCF) of 51400 and 51405 is 5.

GCF(51400,51405) = 5

We will now calculate the prime factors of 51400 and 51405, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51400 and 51405.

How to find the GCF of 51400 and 51405?

We will first find the prime factorization of 51400 and 51405. After we will calculate the factors of 51400 and 51405 and find the biggest common factor number .

Step-1: Prime Factorization of 51400

Prime factors of 51400 are 2, 5, 257. Prime factorization of 51400 in exponential form is:

51400 = 2³ × 5² × 257¹

Step-2: Prime Factorization of 51405

Prime factors of 51405 are 3, 5, 23, 149. Prime factorization of 51405 in exponential form is:

51405 = 3¹ × 5¹ × 23¹ × 149¹

Step-3: Factors of 51400

List of positive integer factors of 51400 that divides 51400 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 257, 514, 1028, 1285, 2056, 2570, 5140, 6425, 10280, 12850, 25700

Step-4: Factors of 51405

List of positive integer factors of 51405 that divides 51400 without a remainder.

1, 3, 5, 15, 23, 69, 115, 149, 345, 447, 745, 2235, 3427, 10281, 17135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51400 and 51405. The biggest common factor number is the GCF number.
So the greatest common factor 51400 and 51405 is 5.

Also check out the Least Common Multiple of 51400 and 51405