What is the Greatest Common Factor of 36705 and 36720?

Greatest common factor (GCF) of 36705 and 36720 is 15.

GCF(36705,36720) = 15

We will now calculate the prime factors of 36705 and 36720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36705 and 36720.

How to find the GCF of 36705 and 36720?

We will first find the prime factorization of 36705 and 36720. After we will calculate the factors of 36705 and 36720 and find the biggest common factor number .

Step-1: Prime Factorization of 36705

Prime factors of 36705 are 3, 5, 2447. Prime factorization of 36705 in exponential form is:

36705 = 3¹ × 5¹ × 2447¹

Step-2: Prime Factorization of 36720

Prime factors of 36720 are 2, 3, 5, 17. Prime factorization of 36720 in exponential form is:

36720 = 2⁴ × 3³ × 5¹ × 17¹

Step-3: Factors of 36705

List of positive integer factors of 36705 that divides 36705 without a remainder.

1, 3, 5, 15, 2447, 7341, 12235

Step-4: Factors of 36720

List of positive integer factors of 36720 that divides 36705 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 27, 30, 34, 36, 40, 45, 48, 51, 54, 60, 68, 72, 80, 85, 90, 102, 108, 120, 135, 136, 144, 153, 170, 180, 204, 216, 240, 255, 270, 272, 306, 340, 360, 408, 432, 459, 510, 540, 612, 680, 720, 765, 816, 918, 1020, 1080, 1224, 1360, 1530, 1836, 2040, 2160, 2295, 2448, 3060, 3672, 4080, 4590, 6120, 7344, 9180, 12240, 18360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36705 and 36720. The biggest common factor number is the GCF number.
So the greatest common factor 36705 and 36720 is 15.

Also check out the Least Common Multiple of 36705 and 36720