What is the Greatest Common Factor of 32768 and 32782?

Greatest common factor (GCF) of 32768 and 32782 is 2.

GCF(32768,32782) = 2

We will now calculate the prime factors of 32768 and 32782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32768 and 32782.

How to find the GCF of 32768 and 32782?

We will first find the prime factorization of 32768 and 32782. After we will calculate the factors of 32768 and 32782 and find the biggest common factor number .

Step-1: Prime Factorization of 32768

Prime factors of 32768 are 2. Prime factorization of 32768 in exponential form is:

32768 = 2¹⁵

Step-2: Prime Factorization of 32782

Prime factors of 32782 are 2, 37, 443. Prime factorization of 32782 in exponential form is:

32782 = 2¹ × 37¹ × 443¹

Step-3: Factors of 32768

List of positive integer factors of 32768 that divides 32768 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384

Step-4: Factors of 32782

List of positive integer factors of 32782 that divides 32768 without a remainder.

1, 2, 37, 74, 443, 886, 16391

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32768 and 32782. The biggest common factor number is the GCF number.
So the greatest common factor 32768 and 32782 is 2.

Also check out the Least Common Multiple of 32768 and 32782