What is the Greatest Common Factor of 750 and 770?

Greatest common factor (GCF) of 750 and 770 is 10.

GCF(750,770) = 10

We will now calculate the prime factors of 750 and 770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 750 and 770.

How to find the GCF of 750 and 770?

We will first find the prime factorization of 750 and 770. After we will calculate the factors of 750 and 770 and find the biggest common factor number .

Step-1: Prime Factorization of 750

Prime factors of 750 are 2, 3, 5. Prime factorization of 750 in exponential form is:

750 = 2¹ × 3¹ × 5³

Step-2: 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-3: Factors of 750

List of positive integer factors of 750 that divides 750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375

Step-4: Factors of 770

List of positive integer factors of 770 that divides 750 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 750 and 770. The biggest common factor number is the GCF number.
So the greatest common factor 750 and 770 is 10.

Also check out the Least Common Multiple of 750 and 770