What is the Greatest Common Factor of 38305 and 38320?

Greatest common factor (GCF) of 38305 and 38320 is 5.

GCF(38305,38320) = 5

We will now calculate the prime factors of 38305 and 38320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38305 and 38320.

How to find the GCF of 38305 and 38320?

We will first find the prime factorization of 38305 and 38320. After we will calculate the factors of 38305 and 38320 and find the biggest common factor number .

Step-1: Prime Factorization of 38305

Prime factors of 38305 are 5, 47, 163. Prime factorization of 38305 in exponential form is:

38305 = 5¹ × 47¹ × 163¹

Step-2: Prime Factorization of 38320

Prime factors of 38320 are 2, 5, 479. Prime factorization of 38320 in exponential form is:

38320 = 2⁴ × 5¹ × 479¹

Step-3: Factors of 38305

List of positive integer factors of 38305 that divides 38305 without a remainder.

1, 5, 47, 163, 235, 815, 7661

Step-4: Factors of 38320

List of positive integer factors of 38320 that divides 38305 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 479, 958, 1916, 2395, 3832, 4790, 7664, 9580, 19160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38305 and 38320. The biggest common factor number is the GCF number.
So the greatest common factor 38305 and 38320 is 5.

Also check out the Least Common Multiple of 38305 and 38320