What is the Greatest Common Factor of 30496 and 30504?

Greatest common factor (GCF) of 30496 and 30504 is 8.

GCF(30496,30504) = 8

We will now calculate the prime factors of 30496 and 30504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30496 and 30504.

How to find the GCF of 30496 and 30504?

We will first find the prime factorization of 30496 and 30504. After we will calculate the factors of 30496 and 30504 and find the biggest common factor number .

Step-1: Prime Factorization of 30496

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

30496 = 2⁵ × 953¹

Step-2: Prime Factorization of 30504

Prime factors of 30504 are 2, 3, 31, 41. Prime factorization of 30504 in exponential form is:

30504 = 2³ × 3¹ × 31¹ × 41¹

Step-3: Factors of 30496

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

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

Step-4: Factors of 30504

List of positive integer factors of 30504 that divides 30496 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 31, 41, 62, 82, 93, 123, 124, 164, 186, 246, 248, 328, 372, 492, 744, 984, 1271, 2542, 3813, 5084, 7626, 10168, 15252

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30496 and 30504. The biggest common factor number is the GCF number.
So the greatest common factor 30496 and 30504 is 8.

Also check out the Least Common Multiple of 30496 and 30504