What is the Greatest Common Factor of 30784 and 30800?

Greatest common factor (GCF) of 30784 and 30800 is 16.

GCF(30784,30800) = 16

We will now calculate the prime factors of 30784 and 30800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30784 and 30800.

How to find the GCF of 30784 and 30800?

We will first find the prime factorization of 30784 and 30800. After we will calculate the factors of 30784 and 30800 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 30800

Prime factors of 30800 are 2, 5, 7, 11. Prime factorization of 30800 in exponential form is:

30800 = 2⁴ × 5² × 7¹ × 11¹

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 30800

List of positive integer factors of 30800 that divides 30784 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 25, 28, 35, 40, 44, 50, 55, 56, 70, 77, 80, 88, 100, 110, 112, 140, 154, 175, 176, 200, 220, 275, 280, 308, 350, 385, 400, 440, 550, 560, 616, 700, 770, 880, 1100, 1232, 1400, 1540, 1925, 2200, 2800, 3080, 3850, 4400, 6160, 7700, 15400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30784 and 30800. The biggest common factor number is the GCF number.
So the greatest common factor 30784 and 30800 is 16.

Also check out the Least Common Multiple of 30784 and 30800