What is the Greatest Common Factor of 32256 and 32270?

Greatest common factor (GCF) of 32256 and 32270 is 14.

GCF(32256,32270) = 14

We will now calculate the prime factors of 32256 and 32270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32256 and 32270.

How to find the GCF of 32256 and 32270?

We will first find the prime factorization of 32256 and 32270. After we will calculate the factors of 32256 and 32270 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 32270

Prime factors of 32270 are 2, 5, 7, 461. Prime factorization of 32270 in exponential form is:

32270 = 2¹ × 5¹ × 7¹ × 461¹

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 32270

List of positive integer factors of 32270 that divides 32256 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 461, 922, 2305, 3227, 4610, 6454, 16135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32256 and 32270. The biggest common factor number is the GCF number.
So the greatest common factor 32256 and 32270 is 14.

Also check out the Least Common Multiple of 32256 and 32270