What is the Greatest Common Factor of 32250 and 32256?

Greatest common factor (GCF) of 32250 and 32256 is 6.

GCF(32250,32256) = 6

We will now calculate the prime factors of 32250 and 32256, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32250 and 32256.

How to find the GCF of 32250 and 32256?

We will first find the prime factorization of 32250 and 32256. After we will calculate the factors of 32250 and 32256 and find the biggest common factor number .

Step-1: Prime Factorization of 32250

Prime factors of 32250 are 2, 3, 5, 43. Prime factorization of 32250 in exponential form is:

32250 = 2¹ × 3¹ × 5³ × 43¹

Step-2: Prime Factorization of 32256

Prime factors of 32256 are 2, 3, 7. Prime factorization of 32256 in exponential form is:

32256 = 2⁹ × 3² × 7¹

Step-3: Factors of 32250

List of positive integer factors of 32250 that divides 32250 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 43, 50, 75, 86, 125, 129, 150, 215, 250, 258, 375, 430, 645, 750, 1075, 1290, 2150, 3225, 5375, 6450, 10750, 16125

Step-4: Factors of 32256

List of positive integer factors of 32256 that divides 32250 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 256, 288, 336, 384, 448, 504, 512, 576, 672, 768, 896, 1008, 1152, 1344, 1536, 1792, 2016, 2304, 2688, 3584, 4032, 4608, 5376, 8064, 10752, 16128

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32250 and 32256. The biggest common factor number is the GCF number.
So the greatest common factor 32250 and 32256 is 6.

Also check out the Least Common Multiple of 32250 and 32256