What is the Greatest Common Factor of 38624 and 38628?

Greatest common factor (GCF) of 38624 and 38628 is 4.

GCF(38624,38628) = 4

We will now calculate the prime factors of 38624 and 38628, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38624 and 38628.

How to find the GCF of 38624 and 38628?

We will first find the prime factorization of 38624 and 38628. After we will calculate the factors of 38624 and 38628 and find the biggest common factor number .

Step-1: Prime Factorization of 38624

Prime factors of 38624 are 2, 17, 71. Prime factorization of 38624 in exponential form is:

38624 = 2⁵ × 17¹ × 71¹

Step-2: Prime Factorization of 38628

Prime factors of 38628 are 2, 3, 29, 37. Prime factorization of 38628 in exponential form is:

38628 = 2² × 3² × 29¹ × 37¹

Step-3: Factors of 38624

List of positive integer factors of 38624 that divides 38624 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 68, 71, 136, 142, 272, 284, 544, 568, 1136, 1207, 2272, 2414, 4828, 9656, 19312

Step-4: Factors of 38628

List of positive integer factors of 38628 that divides 38624 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 29, 36, 37, 58, 74, 87, 111, 116, 148, 174, 222, 261, 333, 348, 444, 522, 666, 1044, 1073, 1332, 2146, 3219, 4292, 6438, 9657, 12876, 19314

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38624 and 38628. The biggest common factor number is the GCF number.
So the greatest common factor 38624 and 38628 is 4.

Also check out the Least Common Multiple of 38624 and 38628