What is the Greatest Common Factor of 30612 and 30624?

Greatest common factor (GCF) of 30612 and 30624 is 12.

GCF(30612,30624) = 12

We will now calculate the prime factors of 30612 and 30624, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30612 and 30624.

How to find the GCF of 30612 and 30624?

We will first find the prime factorization of 30612 and 30624. After we will calculate the factors of 30612 and 30624 and find the biggest common factor number .

Step-1: Prime Factorization of 30612

Prime factors of 30612 are 2, 3, 2551. Prime factorization of 30612 in exponential form is:

30612 = 2² × 3¹ × 2551¹

Step-2: Prime Factorization of 30624

Prime factors of 30624 are 2, 3, 11, 29. Prime factorization of 30624 in exponential form is:

30624 = 2⁵ × 3¹ × 11¹ × 29¹

Step-3: Factors of 30612

List of positive integer factors of 30612 that divides 30612 without a remainder.

1, 2, 3, 4, 6, 12, 2551, 5102, 7653, 10204, 15306

Step-4: Factors of 30624

List of positive integer factors of 30624 that divides 30612 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 29, 32, 33, 44, 48, 58, 66, 87, 88, 96, 116, 132, 174, 176, 232, 264, 319, 348, 352, 464, 528, 638, 696, 928, 957, 1056, 1276, 1392, 1914, 2552, 2784, 3828, 5104, 7656, 10208, 15312

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30612 and 30624. The biggest common factor number is the GCF number.
So the greatest common factor 30612 and 30624 is 12.

Also check out the Least Common Multiple of 30612 and 30624