What is the Greatest Common Factor of 765 and 780?

Greatest common factor (GCF) of 765 and 780 is 15.

GCF(765,780) = 15

We will now calculate the prime factors of 765 and 780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 765 and 780.

How to find the GCF of 765 and 780?

We will first find the prime factorization of 765 and 780. After we will calculate the factors of 765 and 780 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 780

Prime factors of 780 are 2, 3, 5, 13. Prime factorization of 780 in exponential form is:

780 = 2² × 3¹ × 5¹ × 13¹

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 780

List of positive integer factors of 780 that divides 765 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 765 and 780. The biggest common factor number is the GCF number.
So the greatest common factor 765 and 780 is 15.

Also check out the Least Common Multiple of 765 and 780