What is the Greatest Common Factor of 38208 and 38224?

Greatest common factor (GCF) of 38208 and 38224 is 16.

GCF(38208,38224) = 16

We will now calculate the prime factors of 38208 and 38224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38208 and 38224.

How to find the GCF of 38208 and 38224?

We will first find the prime factorization of 38208 and 38224. After we will calculate the factors of 38208 and 38224 and find the biggest common factor number .

Step-1: Prime Factorization of 38208

Prime factors of 38208 are 2, 3, 199. Prime factorization of 38208 in exponential form is:

38208 = 2⁶ × 3¹ × 199¹

Step-2: Prime Factorization of 38224

Prime factors of 38224 are 2, 2389. Prime factorization of 38224 in exponential form is:

38224 = 2⁴ × 2389¹

Step-3: Factors of 38208

List of positive integer factors of 38208 that divides 38208 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 199, 398, 597, 796, 1194, 1592, 2388, 3184, 4776, 6368, 9552, 12736, 19104

Step-4: Factors of 38224

List of positive integer factors of 38224 that divides 38208 without a remainder.

1, 2, 4, 8, 16, 2389, 4778, 9556, 19112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38208 and 38224. The biggest common factor number is the GCF number.
So the greatest common factor 38208 and 38224 is 16.

Also check out the Least Common Multiple of 38208 and 38224