What is the Greatest Common Factor of 770 and 774?

Greatest common factor (GCF) of 770 and 774 is 2.

GCF(770,774) = 2

We will now calculate the prime factors of 770 and 774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 770 and 774.

How to find the GCF of 770 and 774?

We will first find the prime factorization of 770 and 774. After we will calculate the factors of 770 and 774 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 774

Prime factors of 774 are 2, 3, 43. Prime factorization of 774 in exponential form is:

774 = 2¹ × 3² × 43¹

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 774

List of positive integer factors of 774 that divides 770 without a remainder.

1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 770 and 774. The biggest common factor number is the GCF number.
So the greatest common factor 770 and 774 is 2.

Also check out the Least Common Multiple of 770 and 774