What is the Greatest Common Factor of 763 and 777?

Greatest common factor (GCF) of 763 and 777 is 7.

GCF(763,777) = 7

We will now calculate the prime factors of 763 and 777, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 763 and 777.

How to find the GCF of 763 and 777?

We will first find the prime factorization of 763 and 777. After we will calculate the factors of 763 and 777 and find the biggest common factor number .

Step-1: Prime Factorization of 763

Prime factors of 763 are 7, 109. Prime factorization of 763 in exponential form is:

763 = 7¹ × 109¹

Step-2: Prime Factorization of 777

Prime factors of 777 are 3, 7, 37. Prime factorization of 777 in exponential form is:

777 = 3¹ × 7¹ × 37¹

Step-3: Factors of 763

List of positive integer factors of 763 that divides 763 without a remainder.

1, 7, 109

Step-4: Factors of 777

List of positive integer factors of 777 that divides 763 without a remainder.

1, 3, 7, 21, 37, 111, 259

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 763 and 777. The biggest common factor number is the GCF number.
So the greatest common factor 763 and 777 is 7.

Also check out the Least Common Multiple of 763 and 777