What is the Greatest Common Factor of 48720 and 48735?

Greatest common factor (GCF) of 48720 and 48735 is 15.

GCF(48720,48735) = 15

We will now calculate the prime factors of 48720 and 48735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48720 and 48735.

How to find the GCF of 48720 and 48735?

We will first find the prime factorization of 48720 and 48735. After we will calculate the factors of 48720 and 48735 and find the biggest common factor number .

Step-1: Prime Factorization of 48720

Prime factors of 48720 are 2, 3, 5, 7, 29. Prime factorization of 48720 in exponential form is:

48720 = 2⁴ × 3¹ × 5¹ × 7¹ × 29¹

Step-2: Prime Factorization of 48735

Prime factors of 48735 are 3, 5, 19. Prime factorization of 48735 in exponential form is:

48735 = 3³ × 5¹ × 19²

Step-3: Factors of 48720

List of positive integer factors of 48720 that divides 48720 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 29, 30, 35, 40, 42, 48, 56, 58, 60, 70, 80, 84, 87, 105, 112, 116, 120, 140, 145, 168, 174, 203, 210, 232, 240, 280, 290, 336, 348, 406, 420, 435, 464, 560, 580, 609, 696, 812, 840, 870, 1015, 1160, 1218, 1392, 1624, 1680, 1740, 2030, 2320, 2436, 3045, 3248, 3480, 4060, 4872, 6090, 6960, 8120, 9744, 12180, 16240, 24360

Step-4: Factors of 48735

List of positive integer factors of 48735 that divides 48720 without a remainder.

1, 3, 5, 9, 15, 19, 27, 45, 57, 95, 135, 171, 285, 361, 513, 855, 1083, 1805, 2565, 3249, 5415, 9747, 16245

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48720 and 48735. The biggest common factor number is the GCF number.
So the greatest common factor 48720 and 48735 is 15.

Also check out the Least Common Multiple of 48720 and 48735