What is the Greatest Common Factor of 720 and 730?

Greatest common factor (GCF) of 720 and 730 is 10.

GCF(720,730) = 10

We will now calculate the prime factors of 720 and 730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 720 and 730.

How to find the GCF of 720 and 730?

We will first find the prime factorization of 720 and 730. After we will calculate the factors of 720 and 730 and find the biggest common factor number .

Step-1: Prime Factorization of 720

Prime factors of 720 are 2, 3, 5. Prime factorization of 720 in exponential form is:

720 = 2⁴ × 3² × 5¹

Step-2: 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-3: Factors of 720

List of positive integer factors of 720 that divides 720 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360

Step-4: Factors of 730

List of positive integer factors of 730 that divides 720 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 720 and 730. The biggest common factor number is the GCF number.
So the greatest common factor 720 and 730 is 10.

Also check out the Least Common Multiple of 720 and 730