What is the Greatest Common Factor of 30768 and 30784?

Greatest common factor (GCF) of 30768 and 30784 is 16.

GCF(30768,30784) = 16

We will now calculate the prime factors of 30768 and 30784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30768 and 30784.

How to find the GCF of 30768 and 30784?

We will first find the prime factorization of 30768 and 30784. After we will calculate the factors of 30768 and 30784 and find the biggest common factor number .

Step-1: Prime Factorization of 30768

Prime factors of 30768 are 2, 3, 641. Prime factorization of 30768 in exponential form is:

30768 = 2⁴ × 3¹ × 641¹

Step-2: Prime Factorization of 30784

Prime factors of 30784 are 2, 13, 37. Prime factorization of 30784 in exponential form is:

30784 = 2⁶ × 13¹ × 37¹

Step-3: Factors of 30768

List of positive integer factors of 30768 that divides 30768 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 641, 1282, 1923, 2564, 3846, 5128, 7692, 10256, 15384

Step-4: Factors of 30784

List of positive integer factors of 30784 that divides 30768 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 37, 52, 64, 74, 104, 148, 208, 296, 416, 481, 592, 832, 962, 1184, 1924, 2368, 3848, 7696, 15392

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30768 and 30784. The biggest common factor number is the GCF number.
So the greatest common factor 30768 and 30784 is 16.

Also check out the Least Common Multiple of 30768 and 30784