What is the Greatest Common Factor of 730 and 735?

Greatest common factor (GCF) of 730 and 735 is 5.

GCF(730,735) = 5

We will now calculate the prime factors of 730 and 735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 730 and 735.

How to find the GCF of 730 and 735?

We will first find the prime factorization of 730 and 735. After we will calculate the factors of 730 and 735 and find the biggest common factor number .

Step-1: Prime Factorization of 730

Prime factors of 730 are 2, 5, 73. Prime factorization of 730 in exponential form is:

730 = 2¹ × 5¹ × 73¹

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 730

List of positive integer factors of 730 that divides 730 without a remainder.

1, 2, 5, 10, 73, 146, 365

Step-4: Factors of 735

List of positive integer factors of 735 that divides 730 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 730 and 735. The biggest common factor number is the GCF number.
So the greatest common factor 730 and 735 is 5.

Also check out the Least Common Multiple of 730 and 735