What is the Greatest Common Factor of 38250 and 38256?

Greatest common factor (GCF) of 38250 and 38256 is 6.

GCF(38250,38256) = 6

We will now calculate the prime factors of 38250 and 38256, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38250 and 38256.

How to find the GCF of 38250 and 38256?

We will first find the prime factorization of 38250 and 38256. After we will calculate the factors of 38250 and 38256 and find the biggest common factor number .

Step-1: Prime Factorization of 38250

Prime factors of 38250 are 2, 3, 5, 17. Prime factorization of 38250 in exponential form is:

38250 = 2¹ × 3² × 5³ × 17¹

Step-2: 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-3: Factors of 38250

List of positive integer factors of 38250 that divides 38250 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 25, 30, 34, 45, 50, 51, 75, 85, 90, 102, 125, 150, 153, 170, 225, 250, 255, 306, 375, 425, 450, 510, 750, 765, 850, 1125, 1275, 1530, 2125, 2250, 2550, 3825, 4250, 6375, 7650, 12750, 19125

Step-4: Factors of 38256

List of positive integer factors of 38256 that divides 38250 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38250 and 38256. The biggest common factor number is the GCF number.
So the greatest common factor 38250 and 38256 is 6.

Also check out the Least Common Multiple of 38250 and 38256