What is the Greatest Common Factor of 32766 and 32774?

Greatest common factor (GCF) of 32766 and 32774 is 2.

GCF(32766,32774) = 2

We will now calculate the prime factors of 32766 and 32774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32766 and 32774.

How to find the GCF of 32766 and 32774?

We will first find the prime factorization of 32766 and 32774. After we will calculate the factors of 32766 and 32774 and find the biggest common factor number .

Step-1: Prime Factorization of 32766

Prime factors of 32766 are 2, 3, 43, 127. Prime factorization of 32766 in exponential form is:

32766 = 2¹ × 3¹ × 43¹ × 127¹

Step-2: Prime Factorization of 32774

Prime factors of 32774 are 2, 7, 2341. Prime factorization of 32774 in exponential form is:

32774 = 2¹ × 7¹ × 2341¹

Step-3: Factors of 32766

List of positive integer factors of 32766 that divides 32766 without a remainder.

1, 2, 3, 6, 43, 86, 127, 129, 254, 258, 381, 762, 5461, 10922, 16383

Step-4: Factors of 32774

List of positive integer factors of 32774 that divides 32766 without a remainder.

1, 2, 7, 14, 2341, 4682, 16387

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32766 and 32774. The biggest common factor number is the GCF number.
So the greatest common factor 32766 and 32774 is 2.

Also check out the Least Common Multiple of 32766 and 32774