What is the Greatest Common Factor of 705 and 720?

Greatest common factor (GCF) of 705 and 720 is 15.

GCF(705,720) = 15

We will now calculate the prime factors of 705 and 720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 705 and 720.

How to find the GCF of 705 and 720?

We will first find the prime factorization of 705 and 720. After we will calculate the factors of 705 and 720 and find the biggest common factor number .

Step-1: Prime Factorization of 705

Prime factors of 705 are 3, 5, 47. Prime factorization of 705 in exponential form is:

705 = 3¹ × 5¹ × 47¹

Step-2: 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-3: Factors of 705

List of positive integer factors of 705 that divides 705 without a remainder.

1, 3, 5, 15, 47, 141, 235

Step-4: Factors of 720

List of positive integer factors of 720 that divides 705 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 705 and 720. The biggest common factor number is the GCF number.
So the greatest common factor 705 and 720 is 15.

Also check out the Least Common Multiple of 705 and 720