What is the Greatest Common Factor of 765 and 771?

Greatest common factor (GCF) of 765 and 771 is 3.

GCF(765,771) = 3

We will now calculate the prime factors of 765 and 771, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 765 and 771.

How to find the GCF of 765 and 771?

We will first find the prime factorization of 765 and 771. After we will calculate the factors of 765 and 771 and find the biggest common factor number .

Step-1: Prime Factorization of 765

Prime factors of 765 are 3, 5, 17. Prime factorization of 765 in exponential form is:

765 = 3² × 5¹ × 17¹

Step-2: Prime Factorization of 771

Prime factors of 771 are 3, 257. Prime factorization of 771 in exponential form is:

771 = 3¹ × 257¹

Step-3: Factors of 765

List of positive integer factors of 765 that divides 765 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255

Step-4: Factors of 771

List of positive integer factors of 771 that divides 765 without a remainder.

1, 3, 257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 765 and 771. The biggest common factor number is the GCF number.
So the greatest common factor 765 and 771 is 3.

Also check out the Least Common Multiple of 765 and 771