What is the Greatest Common Factor of 30480 and 30496?

Greatest common factor (GCF) of 30480 and 30496 is 16.

GCF(30480,30496) = 16

We will now calculate the prime factors of 30480 and 30496, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30480 and 30496.

How to find the GCF of 30480 and 30496?

We will first find the prime factorization of 30480 and 30496. After we will calculate the factors of 30480 and 30496 and find the biggest common factor number .

Step-1: Prime Factorization of 30480

Prime factors of 30480 are 2, 3, 5, 127. Prime factorization of 30480 in exponential form is:

30480 = 2⁴ × 3¹ × 5¹ × 127¹

Step-2: Prime Factorization of 30496

Prime factors of 30496 are 2, 953. Prime factorization of 30496 in exponential form is:

30496 = 2⁵ × 953¹

Step-3: Factors of 30480

List of positive integer factors of 30480 that divides 30480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 127, 240, 254, 381, 508, 635, 762, 1016, 1270, 1524, 1905, 2032, 2540, 3048, 3810, 5080, 6096, 7620, 10160, 15240

Step-4: Factors of 30496

List of positive integer factors of 30496 that divides 30480 without a remainder.

1, 2, 4, 8, 16, 32, 953, 1906, 3812, 7624, 15248

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30480 and 30496. The biggest common factor number is the GCF number.
So the greatest common factor 30480 and 30496 is 16.

Also check out the Least Common Multiple of 30480 and 30496