What is the Greatest Common Factor of 32768 and 32788?

Greatest common factor (GCF) of 32768 and 32788 is 4.

GCF(32768,32788) = 4

We will now calculate the prime factors of 32768 and 32788, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32768 and 32788.

How to find the GCF of 32768 and 32788?

We will first find the prime factorization of 32768 and 32788. After we will calculate the factors of 32768 and 32788 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 32788

Prime factors of 32788 are 2, 7, 1171. Prime factorization of 32788 in exponential form is:

32788 = 2² × 7¹ × 1171¹

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 32788

List of positive integer factors of 32788 that divides 32768 without a remainder.

1, 2, 4, 7, 14, 28, 1171, 2342, 4684, 8197, 16394

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32768 and 32788. The biggest common factor number is the GCF number.
So the greatest common factor 32768 and 32788 is 4.

Also check out the Least Common Multiple of 32768 and 32788