What is the Greatest Common Factor of 765 and 784?

Greatest common factor (GCF) of 765 and 784 is 1.

GCF(765,784) = 1

We will now calculate the prime factors of 765 and 784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 765 and 784.

How to find the GCF of 765 and 784?

We will first find the prime factorization of 765 and 784. After we will calculate the factors of 765 and 784 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 784

Prime factors of 784 are 2, 7. Prime factorization of 784 in exponential form is:

784 = 2⁴ × 7²

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 784

List of positive integer factors of 784 that divides 765 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 765 and 784. The biggest common factor number is the GCF number.
So the greatest common factor 765 and 784 is 1.

Also check out the Least Common Multiple of 765 and 784