What is the Greatest Common Factor of 767 and 784?

Greatest common factor (GCF) of 767 and 784 is 1.

GCF(767,784) = 1

We will now calculate the prime factors of 767 and 784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 767 and 784.

How to find the GCF of 767 and 784?

We will first find the prime factorization of 767 and 784. After we will calculate the factors of 767 and 784 and find the biggest common factor number .

Step-1: Prime Factorization of 767

Prime factors of 767 are 13, 59. Prime factorization of 767 in exponential form is:

767 = 13¹ × 59¹

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 767

List of positive integer factors of 767 that divides 767 without a remainder.

1, 13, 59

Step-4: Factors of 784

List of positive integer factors of 784 that divides 767 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 767 and 784. The biggest common factor number is the GCF number.
So the greatest common factor 767 and 784 is 1.

Also check out the Least Common Multiple of 767 and 784