What is the Greatest Common Factor of 735 and 750?

Greatest common factor (GCF) of 735 and 750 is 15.

GCF(735,750) = 15

We will now calculate the prime factors of 735 and 750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 735 and 750.

How to find the GCF of 735 and 750?

We will first find the prime factorization of 735 and 750. After we will calculate the factors of 735 and 750 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 750

Prime factors of 750 are 2, 3, 5. Prime factorization of 750 in exponential form is:

750 = 2¹ × 3¹ × 5³

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 750

List of positive integer factors of 750 that divides 735 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 735 and 750. The biggest common factor number is the GCF number.
So the greatest common factor 735 and 750 is 15.

Also check out the Least Common Multiple of 735 and 750