What is the Greatest Common Factor of 34816 and 34830?

Greatest common factor (GCF) of 34816 and 34830 is 2.

GCF(34816,34830) = 2

We will now calculate the prime factors of 34816 and 34830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34816 and 34830.

How to find the GCF of 34816 and 34830?

We will first find the prime factorization of 34816 and 34830. After we will calculate the factors of 34816 and 34830 and find the biggest common factor number .

Step-1: Prime Factorization of 34816

Prime factors of 34816 are 2, 17. Prime factorization of 34816 in exponential form is:

34816 = 2¹¹ × 17¹

Step-2: Prime Factorization of 34830

Prime factors of 34830 are 2, 3, 5, 43. Prime factorization of 34830 in exponential form is:

34830 = 2¹ × 3⁴ × 5¹ × 43¹

Step-3: Factors of 34816

List of positive integer factors of 34816 that divides 34816 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 512, 544, 1024, 1088, 2048, 2176, 4352, 8704, 17408

Step-4: Factors of 34830

List of positive integer factors of 34830 that divides 34816 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 43, 45, 54, 81, 86, 90, 129, 135, 162, 215, 258, 270, 387, 405, 430, 645, 774, 810, 1161, 1290, 1935, 2322, 3483, 3870, 5805, 6966, 11610, 17415

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34816 and 34830. The biggest common factor number is the GCF number.
So the greatest common factor 34816 and 34830 is 2.

Also check out the Least Common Multiple of 34816 and 34830