What is the Greatest Common Factor of 14769 and 14784?

Greatest common factor (GCF) of 14769 and 14784 is 3.

GCF(14769,14784) = 3

We will now calculate the prime factors of 14769 and 14784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14769 and 14784.

How to find the GCF of 14769 and 14784?

We will first find the prime factorization of 14769 and 14784. After we will calculate the factors of 14769 and 14784 and find the biggest common factor number .

Step-1: Prime Factorization of 14769

Prime factors of 14769 are 3, 547. Prime factorization of 14769 in exponential form is:

14769 = 3³ × 547¹

Step-2: 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-3: Factors of 14769

List of positive integer factors of 14769 that divides 14769 without a remainder.

1, 3, 9, 27, 547, 1641, 4923

Step-4: Factors of 14784

List of positive integer factors of 14784 that divides 14769 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14769 and 14784. The biggest common factor number is the GCF number.
So the greatest common factor 14769 and 14784 is 3.

Also check out the Least Common Multiple of 14769 and 14784