What is the Greatest Common Factor of 770 and 775?

Greatest common factor (GCF) of 770 and 775 is 5.

GCF(770,775) = 5

We will now calculate the prime factors of 770 and 775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 770 and 775.

How to find the GCF of 770 and 775?

We will first find the prime factorization of 770 and 775. After we will calculate the factors of 770 and 775 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 775

Prime factors of 775 are 5, 31. Prime factorization of 775 in exponential form is:

775 = 5² × 31¹

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 775

List of positive integer factors of 775 that divides 770 without a remainder.

1, 5, 25, 31, 155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 770 and 775. The biggest common factor number is the GCF number.
So the greatest common factor 770 and 775 is 5.

Also check out the Least Common Multiple of 770 and 775