What is the Greatest Common Factor of 18720 and 18735?

Greatest common factor (GCF) of 18720 and 18735 is 15.

GCF(18720,18735) = 15

We will now calculate the prime factors of 18720 and 18735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18720 and 18735.

How to find the GCF of 18720 and 18735?

We will first find the prime factorization of 18720 and 18735. After we will calculate the factors of 18720 and 18735 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 18735

Prime factors of 18735 are 3, 5, 1249. Prime factorization of 18735 in exponential form is:

18735 = 3¹ × 5¹ × 1249¹

Step-3: Factors of 18720

List of positive integer factors of 18720 that divides 18720 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

Step-4: Factors of 18735

List of positive integer factors of 18735 that divides 18720 without a remainder.

1, 3, 5, 15, 1249, 3747, 6245

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18720 and 18735. The biggest common factor number is the GCF number.
So the greatest common factor 18720 and 18735 is 15.

Also check out the Least Common Multiple of 18720 and 18735