What is the Greatest Common Factor of 770 and 777?

Greatest common factor (GCF) of 770 and 777 is 7.

GCF(770,777) = 7

We will now calculate the prime factors of 770 and 777, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 770 and 777.

How to find the GCF of 770 and 777?

We will first find the prime factorization of 770 and 777. After we will calculate the factors of 770 and 777 and find the biggest common factor number .

Step-1: Prime Factorization of 770

Prime factors of 770 are 2, 5, 7, 11. Prime factorization of 770 in exponential form is:

770 = 2¹ × 5¹ × 7¹ × 11¹

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 770

List of positive integer factors of 770 that divides 770 without a remainder.

1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385

Step-4: Factors of 777

List of positive integer factors of 777 that divides 770 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 770 and 777. The biggest common factor number is the GCF number.
So the greatest common factor 770 and 777 is 7.

Also check out the Least Common Multiple of 770 and 777