What is the Greatest Common Factor of 14800 and 14805?

Greatest common factor (GCF) of 14800 and 14805 is 5.

GCF(14800,14805) = 5

We will now calculate the prime factors of 14800 and 14805, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14800 and 14805.

How to find the GCF of 14800 and 14805?

We will first find the prime factorization of 14800 and 14805. After we will calculate the factors of 14800 and 14805 and find the biggest common factor number .

Step-1: Prime Factorization of 14800

Prime factors of 14800 are 2, 5, 37. Prime factorization of 14800 in exponential form is:

14800 = 2⁴ × 5² × 37¹

Step-2: Prime Factorization of 14805

Prime factors of 14805 are 3, 5, 7, 47. Prime factorization of 14805 in exponential form is:

14805 = 3² × 5¹ × 7¹ × 47¹

Step-3: Factors of 14800

List of positive integer factors of 14800 that divides 14800 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 37, 40, 50, 74, 80, 100, 148, 185, 200, 296, 370, 400, 592, 740, 925, 1480, 1850, 2960, 3700, 7400

Step-4: Factors of 14805

List of positive integer factors of 14805 that divides 14800 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 47, 63, 105, 141, 235, 315, 329, 423, 705, 987, 1645, 2115, 2961, 4935

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14800 and 14805. The biggest common factor number is the GCF number.
So the greatest common factor 14800 and 14805 is 5.

Also check out the Least Common Multiple of 14800 and 14805