What is the Greatest Common Factor of 765 and 782?

Greatest common factor (GCF) of 765 and 782 is 17.

GCF(765,782) = 17

We will now calculate the prime factors of 765 and 782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 765 and 782.

How to find the GCF of 765 and 782?

We will first find the prime factorization of 765 and 782. After we will calculate the factors of 765 and 782 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 782

Prime factors of 782 are 2, 17, 23. Prime factorization of 782 in exponential form is:

782 = 2¹ × 17¹ × 23¹

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 782

List of positive integer factors of 782 that divides 765 without a remainder.

1, 2, 17, 23, 34, 46, 391

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 765 and 782. The biggest common factor number is the GCF number.
So the greatest common factor 765 and 782 is 17.

Also check out the Least Common Multiple of 765 and 782