What is the Greatest Common Factor of 750 and 765?

Greatest common factor (GCF) of 750 and 765 is 15.

GCF(750,765) = 15

We will now calculate the prime factors of 750 and 765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 750 and 765.

How to find the GCF of 750 and 765?

We will first find the prime factorization of 750 and 765. After we will calculate the factors of 750 and 765 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 765

Prime factors of 765 are 3, 5, 17. Prime factorization of 765 in exponential form is:

765 = 3² × 5¹ × 17¹

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 765

List of positive integer factors of 765 that divides 750 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 750 and 765. The biggest common factor number is the GCF number.
So the greatest common factor 750 and 765 is 15.

Also check out the Least Common Multiple of 750 and 765