What is the Greatest Common Factor of 38256 and 38274?

Greatest common factor (GCF) of 38256 and 38274 is 6.

GCF(38256,38274) = 6

We will now calculate the prime factors of 38256 and 38274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38256 and 38274.

How to find the GCF of 38256 and 38274?

We will first find the prime factorization of 38256 and 38274. After we will calculate the factors of 38256 and 38274 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 38274

Prime factors of 38274 are 2, 3, 6379. Prime factorization of 38274 in exponential form is:

38274 = 2¹ × 3¹ × 6379¹

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 38274

List of positive integer factors of 38274 that divides 38256 without a remainder.

1, 2, 3, 6, 6379, 12758, 19137

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38256 and 38274. The biggest common factor number is the GCF number.
So the greatest common factor 38256 and 38274 is 6.

Also check out the Least Common Multiple of 38256 and 38274