What is the Greatest Common Factor of 30784 and 30792?

Greatest common factor (GCF) of 30784 and 30792 is 8.

GCF(30784,30792) = 8

We will now calculate the prime factors of 30784 and 30792, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30784 and 30792.

How to find the GCF of 30784 and 30792?

We will first find the prime factorization of 30784 and 30792. After we will calculate the factors of 30784 and 30792 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30792

Prime factors of 30792 are 2, 3, 1283. Prime factorization of 30792 in exponential form is:

30792 = 2³ × 3¹ × 1283¹

Step-3: Factors of 30784

List of positive integer factors of 30784 that divides 30784 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

Step-4: Factors of 30792

List of positive integer factors of 30792 that divides 30784 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1283, 2566, 3849, 5132, 7698, 10264, 15396

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30784 and 30792. The biggest common factor number is the GCF number.
So the greatest common factor 30784 and 30792 is 8.

Also check out the Least Common Multiple of 30784 and 30792