What is the Greatest Common Factor of 18705 and 18720?

Greatest common factor (GCF) of 18705 and 18720 is 15.

GCF(18705,18720) = 15

We will now calculate the prime factors of 18705 and 18720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18705 and 18720.

How to find the GCF of 18705 and 18720?

We will first find the prime factorization of 18705 and 18720. After we will calculate the factors of 18705 and 18720 and find the biggest common factor number .

Step-1: Prime Factorization of 18705

Prime factors of 18705 are 3, 5, 29, 43. Prime factorization of 18705 in exponential form is:

18705 = 3¹ × 5¹ × 29¹ × 43¹

Step-2: Prime Factorization of 18720

Prime factors of 18720 are 2, 3, 5, 13. Prime factorization of 18720 in exponential form is:

18720 = 2⁵ × 3² × 5¹ × 13¹

Step-3: Factors of 18705

List of positive integer factors of 18705 that divides 18705 without a remainder.

1, 3, 5, 15, 29, 43, 87, 129, 145, 215, 435, 645, 1247, 3741, 6235

Step-4: Factors of 18720

List of positive integer factors of 18720 that divides 18705 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 26, 30, 32, 36, 39, 40, 45, 48, 52, 60, 65, 72, 78, 80, 90, 96, 104, 117, 120, 130, 144, 156, 160, 180, 195, 208, 234, 240, 260, 288, 312, 360, 390, 416, 468, 480, 520, 585, 624, 720, 780, 936, 1040, 1170, 1248, 1440, 1560, 1872, 2080, 2340, 3120, 3744, 4680, 6240, 9360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18705 and 18720. The biggest common factor number is the GCF number.
So the greatest common factor 18705 and 18720 is 15.

Also check out the Least Common Multiple of 18705 and 18720