What is the Greatest Common Factor of 30624 and 30629?

Greatest common factor (GCF) of 30624 and 30629 is 1.

GCF(30624,30629) = 1

We will now calculate the prime factors of 30624 and 30629, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30624 and 30629.

How to find the GCF of 30624 and 30629?

We will first find the prime factorization of 30624 and 30629. After we will calculate the factors of 30624 and 30629 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 30629

Prime factors of 30629 are 109, 281. Prime factorization of 30629 in exponential form is:

30629 = 109¹ × 281¹

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 30629

List of positive integer factors of 30629 that divides 30624 without a remainder.

1, 109, 281

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30624 and 30629. The biggest common factor number is the GCF number.
So the greatest common factor 30624 and 30629 is 1.

Also check out the Least Common Multiple of 30624 and 30629