What is the Greatest Common Factor of 747 and 759?

Greatest common factor (GCF) of 747 and 759 is 3.

GCF(747,759) = 3

We will now calculate the prime factors of 747 and 759, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 747 and 759.

How to find the GCF of 747 and 759?

We will first find the prime factorization of 747 and 759. After we will calculate the factors of 747 and 759 and find the biggest common factor number .

Step-1: Prime Factorization of 747

Prime factors of 747 are 3, 83. Prime factorization of 747 in exponential form is:

747 = 3² × 83¹

Step-2: Prime Factorization of 759

Prime factors of 759 are 3, 11, 23. Prime factorization of 759 in exponential form is:

759 = 3¹ × 11¹ × 23¹

Step-3: Factors of 747

List of positive integer factors of 747 that divides 747 without a remainder.

1, 3, 9, 83, 249

Step-4: Factors of 759

List of positive integer factors of 759 that divides 747 without a remainder.

1, 3, 11, 23, 33, 69, 253

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 747 and 759. The biggest common factor number is the GCF number.
So the greatest common factor 747 and 759 is 3.

Also check out the Least Common Multiple of 747 and 759