What is the Greatest Common Factor of 32256 and 32274?

Greatest common factor (GCF) of 32256 and 32274 is 18.

GCF(32256,32274) = 18

We will now calculate the prime factors of 32256 and 32274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32256 and 32274.

How to find the GCF of 32256 and 32274?

We will first find the prime factorization of 32256 and 32274. After we will calculate the factors of 32256 and 32274 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 32274

Prime factors of 32274 are 2, 3, 11, 163. Prime factorization of 32274 in exponential form is:

32274 = 2¹ × 3² × 11¹ × 163¹

Step-3: Factors of 32256

List of positive integer factors of 32256 that divides 32256 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

Step-4: Factors of 32274

List of positive integer factors of 32274 that divides 32256 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 163, 198, 326, 489, 978, 1467, 1793, 2934, 3586, 5379, 10758, 16137

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32256 and 32274. The biggest common factor number is the GCF number.
So the greatest common factor 32256 and 32274 is 18.

Also check out the Least Common Multiple of 32256 and 32274