What is the Greatest Common Factor of 48300 and 48315?

Greatest common factor (GCF) of 48300 and 48315 is 15.

GCF(48300,48315) = 15

We will now calculate the prime factors of 48300 and 48315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48300 and 48315.

How to find the GCF of 48300 and 48315?

We will first find the prime factorization of 48300 and 48315. After we will calculate the factors of 48300 and 48315 and find the biggest common factor number .

Step-1: Prime Factorization of 48300

Prime factors of 48300 are 2, 3, 5, 7, 23. Prime factorization of 48300 in exponential form is:

48300 = 2² × 3¹ × 5² × 7¹ × 23¹

Step-2: Prime Factorization of 48315

Prime factors of 48315 are 3, 5, 3221. Prime factorization of 48315 in exponential form is:

48315 = 3¹ × 5¹ × 3221¹

Step-3: Factors of 48300

List of positive integer factors of 48300 that divides 48300 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 25, 28, 30, 35, 42, 46, 50, 60, 69, 70, 75, 84, 92, 100, 105, 115, 138, 140, 150, 161, 175, 210, 230, 276, 300, 322, 345, 350, 420, 460, 483, 525, 575, 644, 690, 700, 805, 966, 1050, 1150, 1380, 1610, 1725, 1932, 2100, 2300, 2415, 3220, 3450, 4025, 4830, 6900, 8050, 9660, 12075, 16100, 24150

Step-4: Factors of 48315

List of positive integer factors of 48315 that divides 48300 without a remainder.

1, 3, 5, 15, 3221, 9663, 16105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48300 and 48315. The biggest common factor number is the GCF number.
So the greatest common factor 48300 and 48315 is 15.

Also check out the Least Common Multiple of 48300 and 48315