What is the Greatest Common Factor of 735 and 744?

Greatest common factor (GCF) of 735 and 744 is 3.

GCF(735,744) = 3

We will now calculate the prime factors of 735 and 744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 735 and 744.

How to find the GCF of 735 and 744?

We will first find the prime factorization of 735 and 744. After we will calculate the factors of 735 and 744 and find the biggest common factor number .

Step-1: Prime Factorization of 735

Prime factors of 735 are 3, 5, 7. Prime factorization of 735 in exponential form is:

735 = 3¹ × 5¹ × 7²

Step-2: Prime Factorization of 744

Prime factors of 744 are 2, 3, 31. Prime factorization of 744 in exponential form is:

744 = 2³ × 3¹ × 31¹

Step-3: Factors of 735

List of positive integer factors of 735 that divides 735 without a remainder.

1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245

Step-4: Factors of 744

List of positive integer factors of 744 that divides 735 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 735 and 744. The biggest common factor number is the GCF number.
So the greatest common factor 735 and 744 is 3.

Also check out the Least Common Multiple of 735 and 744