What is the Greatest Common Factor of 14784 and 14800?

Greatest common factor (GCF) of 14784 and 14800 is 16.

GCF(14784,14800) = 16

We will now calculate the prime factors of 14784 and 14800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14784 and 14800.

How to find the GCF of 14784 and 14800?

We will first find the prime factorization of 14784 and 14800. After we will calculate the factors of 14784 and 14800 and find the biggest common factor number .

Step-1: Prime Factorization of 14784

Prime factors of 14784 are 2, 3, 7, 11. Prime factorization of 14784 in exponential form is:

14784 = 2⁶ × 3¹ × 7¹ × 11¹

Step-2: 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-3: Factors of 14784

List of positive integer factors of 14784 that divides 14784 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 32, 33, 42, 44, 48, 56, 64, 66, 77, 84, 88, 96, 112, 132, 154, 168, 176, 192, 224, 231, 264, 308, 336, 352, 448, 462, 528, 616, 672, 704, 924, 1056, 1232, 1344, 1848, 2112, 2464, 3696, 4928, 7392

Step-4: Factors of 14800

List of positive integer factors of 14800 that divides 14784 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14784 and 14800. The biggest common factor number is the GCF number.
So the greatest common factor 14784 and 14800 is 16.

Also check out the Least Common Multiple of 14784 and 14800