What is the Greatest Common Factor of 48720 and 48729?

Greatest common factor (GCF) of 48720 and 48729 is 3.

GCF(48720,48729) = 3

We will now calculate the prime factors of 48720 and 48729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48720 and 48729.

How to find the GCF of 48720 and 48729?

We will first find the prime factorization of 48720 and 48729. After we will calculate the factors of 48720 and 48729 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 48729

Prime factors of 48729 are 3, 37, 439. Prime factorization of 48729 in exponential form is:

48729 = 3¹ × 37¹ × 439¹

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 48729

List of positive integer factors of 48729 that divides 48720 without a remainder.

1, 3, 37, 111, 439, 1317, 16243

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48720 and 48729. The biggest common factor number is the GCF number.
So the greatest common factor 48720 and 48729 is 3.

Also check out the Least Common Multiple of 48720 and 48729