What is the Greatest Common Factor of 731 and 735?

Greatest common factor (GCF) of 731 and 735 is 1.

GCF(731,735) = 1

We will now calculate the prime factors of 731 and 735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 731 and 735.

How to find the GCF of 731 and 735?

We will first find the prime factorization of 731 and 735. After we will calculate the factors of 731 and 735 and find the biggest common factor number .

Step-1: Prime Factorization of 731

Prime factors of 731 are 17, 43. Prime factorization of 731 in exponential form is:

731 = 17¹ × 43¹

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 731

List of positive integer factors of 731 that divides 731 without a remainder.

1, 17, 43

Step-4: Factors of 735

List of positive integer factors of 735 that divides 731 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 731 and 735. The biggest common factor number is the GCF number.
So the greatest common factor 731 and 735 is 1.

Also check out the Least Common Multiple of 731 and 735