What is the Greatest Common Factor of 32754 and 32768?

Greatest common factor (GCF) of 32754 and 32768 is 2.

GCF(32754,32768) = 2

We will now calculate the prime factors of 32754 and 32768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32754 and 32768.

How to find the GCF of 32754 and 32768?

We will first find the prime factorization of 32754 and 32768. After we will calculate the factors of 32754 and 32768 and find the biggest common factor number .

Step-1: Prime Factorization of 32754

Prime factors of 32754 are 2, 3, 53, 103. Prime factorization of 32754 in exponential form is:

32754 = 2¹ × 3¹ × 53¹ × 103¹

Step-2: Prime Factorization of 32768

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

32768 = 2¹⁵

Step-3: Factors of 32754

List of positive integer factors of 32754 that divides 32754 without a remainder.

1, 2, 3, 6, 53, 103, 106, 159, 206, 309, 318, 618, 5459, 10918, 16377

Step-4: Factors of 32768

List of positive integer factors of 32768 that divides 32754 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32754 and 32768. The biggest common factor number is the GCF number.
So the greatest common factor 32754 and 32768 is 2.

Also check out the Least Common Multiple of 32754 and 32768