What is the Greatest Common Factor of 766 and 782?

Greatest common factor (GCF) of 766 and 782 is 2.

GCF(766,782) = 2

We will now calculate the prime factors of 766 and 782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 766 and 782.

How to find the GCF of 766 and 782?

We will first find the prime factorization of 766 and 782. After we will calculate the factors of 766 and 782 and find the biggest common factor number .

Step-1: Prime Factorization of 766

Prime factors of 766 are 2, 383. Prime factorization of 766 in exponential form is:

766 = 2¹ × 383¹

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 766

List of positive integer factors of 766 that divides 766 without a remainder.

1, 2, 383

Step-4: Factors of 782

List of positive integer factors of 782 that divides 766 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 766 and 782. The biggest common factor number is the GCF number.
So the greatest common factor 766 and 782 is 2.

Also check out the Least Common Multiple of 766 and 782