What is the Greatest Common Factor of 38208 and 38228?

Greatest common factor (GCF) of 38208 and 38228 is 4.

GCF(38208,38228) = 4

We will now calculate the prime factors of 38208 and 38228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38208 and 38228.

How to find the GCF of 38208 and 38228?

We will first find the prime factorization of 38208 and 38228. After we will calculate the factors of 38208 and 38228 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 38228

Prime factors of 38228 are 2, 19, 503. Prime factorization of 38228 in exponential form is:

38228 = 2² × 19¹ × 503¹

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 38228

List of positive integer factors of 38228 that divides 38208 without a remainder.

1, 2, 4, 19, 38, 76, 503, 1006, 2012, 9557, 19114

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38208 and 38228. The biggest common factor number is the GCF number.
So the greatest common factor 38208 and 38228 is 4.

Also check out the Least Common Multiple of 38208 and 38228