What is the Greatest Common Factor of 765 and 775?

Greatest common factor (GCF) of 765 and 775 is 5.

GCF(765,775) = 5

We will now calculate the prime factors of 765 and 775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 765 and 775.

How to find the GCF of 765 and 775?

We will first find the prime factorization of 765 and 775. After we will calculate the factors of 765 and 775 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 775

Prime factors of 775 are 5, 31. Prime factorization of 775 in exponential form is:

775 = 5² × 31¹

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 775

List of positive integer factors of 775 that divides 765 without a remainder.

1, 5, 25, 31, 155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 765 and 775. The biggest common factor number is the GCF number.
So the greatest common factor 765 and 775 is 5.

Also check out the Least Common Multiple of 765 and 775