What is the Greatest Common Factor of 58624 and 58638?

Greatest common factor (GCF) of 58624 and 58638 is 2.

GCF(58624,58638) = 2

We will now calculate the prime factors of 58624 and 58638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58624 and 58638.

How to find the GCF of 58624 and 58638?

We will first find the prime factorization of 58624 and 58638. After we will calculate the factors of 58624 and 58638 and find the biggest common factor number .

Step-1: Prime Factorization of 58624

Prime factors of 58624 are 2, 229. Prime factorization of 58624 in exponential form is:

58624 = 2⁸ × 229¹

Step-2: Prime Factorization of 58638

Prime factors of 58638 are 2, 3, 29, 337. Prime factorization of 58638 in exponential form is:

58638 = 2¹ × 3¹ × 29¹ × 337¹

Step-3: Factors of 58624

List of positive integer factors of 58624 that divides 58624 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 229, 256, 458, 916, 1832, 3664, 7328, 14656, 29312

Step-4: Factors of 58638

List of positive integer factors of 58638 that divides 58624 without a remainder.

1, 2, 3, 6, 29, 58, 87, 174, 337, 674, 1011, 2022, 9773, 19546, 29319

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58624 and 58638. The biggest common factor number is the GCF number.
So the greatest common factor 58624 and 58638 is 2.

Also check out the Least Common Multiple of 58624 and 58638