What is the Greatest Common Factor of 38256 and 38265?

Greatest common factor (GCF) of 38256 and 38265 is 3.

GCF(38256,38265) = 3

We will now calculate the prime factors of 38256 and 38265, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38256 and 38265.

How to find the GCF of 38256 and 38265?

We will first find the prime factorization of 38256 and 38265. After we will calculate the factors of 38256 and 38265 and find the biggest common factor number .

Step-1: Prime Factorization of 38256

Prime factors of 38256 are 2, 3, 797. Prime factorization of 38256 in exponential form is:

38256 = 2⁴ × 3¹ × 797¹

Step-2: Prime Factorization of 38265

Prime factors of 38265 are 3, 5, 2551. Prime factorization of 38265 in exponential form is:

38265 = 3¹ × 5¹ × 2551¹

Step-3: Factors of 38256

List of positive integer factors of 38256 that divides 38256 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 797, 1594, 2391, 3188, 4782, 6376, 9564, 12752, 19128

Step-4: Factors of 38265

List of positive integer factors of 38265 that divides 38256 without a remainder.

1, 3, 5, 15, 2551, 7653, 12755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38256 and 38265. The biggest common factor number is the GCF number.
So the greatest common factor 38256 and 38265 is 3.

Also check out the Least Common Multiple of 38256 and 38265