What is the Greatest Common Factor of 52305 and 52320?

Greatest common factor (GCF) of 52305 and 52320 is 15.

GCF(52305,52320) = 15

We will now calculate the prime factors of 52305 and 52320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52305 and 52320.

How to find the GCF of 52305 and 52320?

We will first find the prime factorization of 52305 and 52320. After we will calculate the factors of 52305 and 52320 and find the biggest common factor number .

Step-1: Prime Factorization of 52305

Prime factors of 52305 are 3, 5, 11, 317. Prime factorization of 52305 in exponential form is:

52305 = 3¹ × 5¹ × 11¹ × 317¹

Step-2: Prime Factorization of 52320

Prime factors of 52320 are 2, 3, 5, 109. Prime factorization of 52320 in exponential form is:

52320 = 2⁵ × 3¹ × 5¹ × 109¹

Step-3: Factors of 52305

List of positive integer factors of 52305 that divides 52305 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 317, 951, 1585, 3487, 4755, 10461, 17435

Step-4: Factors of 52320

List of positive integer factors of 52320 that divides 52305 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 109, 120, 160, 218, 240, 327, 436, 480, 545, 654, 872, 1090, 1308, 1635, 1744, 2180, 2616, 3270, 3488, 4360, 5232, 6540, 8720, 10464, 13080, 17440, 26160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52305 and 52320. The biggest common factor number is the GCF number.
So the greatest common factor 52305 and 52320 is 15.

Also check out the Least Common Multiple of 52305 and 52320