What is the Greatest Common Factor of 735 and 755?

Greatest common factor (GCF) of 735 and 755 is 5.

GCF(735,755) = 5

We will now calculate the prime factors of 735 and 755, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 735 and 755.

How to find the GCF of 735 and 755?

We will first find the prime factorization of 735 and 755. After we will calculate the factors of 735 and 755 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 755

Prime factors of 755 are 5, 151. Prime factorization of 755 in exponential form is:

755 = 5¹ × 151¹

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 755

List of positive integer factors of 755 that divides 735 without a remainder.

1, 5, 151

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 735 and 755. The biggest common factor number is the GCF number.
So the greatest common factor 735 and 755 is 5.

Also check out the Least Common Multiple of 735 and 755