What is the Greatest Common Factor of 38614 and 38624?

Greatest common factor (GCF) of 38614 and 38624 is 2.

GCF(38614,38624) = 2

We will now calculate the prime factors of 38614 and 38624, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38614 and 38624.

How to find the GCF of 38614 and 38624?

We will first find the prime factorization of 38614 and 38624. After we will calculate the factors of 38614 and 38624 and find the biggest common factor number .

Step-1: Prime Factorization of 38614

Prime factors of 38614 are 2, 43, 449. Prime factorization of 38614 in exponential form is:

38614 = 2¹ × 43¹ × 449¹

Step-2: 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-3: Factors of 38614

List of positive integer factors of 38614 that divides 38614 without a remainder.

1, 2, 43, 86, 449, 898, 19307

Step-4: Factors of 38624

List of positive integer factors of 38624 that divides 38614 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38614 and 38624. The biggest common factor number is the GCF number.
So the greatest common factor 38614 and 38624 is 2.

Also check out the Least Common Multiple of 38614 and 38624