What is the Greatest Common Factor of 729 and 735?

Greatest common factor (GCF) of 729 and 735 is 3.

GCF(729,735) = 3

We will now calculate the prime factors of 729 and 735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 729 and 735.

How to find the GCF of 729 and 735?

We will first find the prime factorization of 729 and 735. After we will calculate the factors of 729 and 735 and find the biggest common factor number .

Step-1: Prime Factorization of 729

Prime factors of 729 are 3. Prime factorization of 729 in exponential form is:

729 = 3⁶

Step-2: 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-3: Factors of 729

List of positive integer factors of 729 that divides 729 without a remainder.

1, 3, 9, 27, 81, 243

Step-4: Factors of 735

List of positive integer factors of 735 that divides 729 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 729 and 735. The biggest common factor number is the GCF number.
So the greatest common factor 729 and 735 is 3.

Also check out the Least Common Multiple of 729 and 735