What is the Greatest Common Factor of 30624 and 30630?

Greatest common factor (GCF) of 30624 and 30630 is 6.

GCF(30624,30630) = 6

We will now calculate the prime factors of 30624 and 30630, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30624 and 30630.

How to find the GCF of 30624 and 30630?

We will first find the prime factorization of 30624 and 30630. After we will calculate the factors of 30624 and 30630 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30630

Prime factors of 30630 are 2, 3, 5, 1021. Prime factorization of 30630 in exponential form is:

30630 = 2¹ × 3¹ × 5¹ × 1021¹

Step-3: Factors of 30624

List of positive integer factors of 30624 that divides 30624 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

Step-4: Factors of 30630

List of positive integer factors of 30630 that divides 30624 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1021, 2042, 3063, 5105, 6126, 10210, 15315

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30624 and 30630. The biggest common factor number is the GCF number.
So the greatest common factor 30624 and 30630 is 6.

Also check out the Least Common Multiple of 30624 and 30630