What is the Greatest Common Factor of 753 and 765?

Greatest common factor (GCF) of 753 and 765 is 3.

GCF(753,765) = 3

We will now calculate the prime factors of 753 and 765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 753 and 765.

How to find the GCF of 753 and 765?

We will first find the prime factorization of 753 and 765. After we will calculate the factors of 753 and 765 and find the biggest common factor number .

Step-1: Prime Factorization of 753

Prime factors of 753 are 3, 251. Prime factorization of 753 in exponential form is:

753 = 3¹ × 251¹

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 753

List of positive integer factors of 753 that divides 753 without a remainder.

1, 3, 251

Step-4: Factors of 765

List of positive integer factors of 765 that divides 753 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 753 and 765. The biggest common factor number is the GCF number.
So the greatest common factor 753 and 765 is 3.

Also check out the Least Common Multiple of 753 and 765