What are the divisors of 4395?

1, 3, 5, 15, 293, 879, 1465, 4395

There is a total of 8 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 882.

8 odd divisors

1, 3, 5, 15, 293, 879, 1465, 4395

How to compute the divisors of 4395?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 4395 by each of the numbers from 1 to 4395 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

4395 / 1 = 4395 (the remainder is 0, so 1 is a divisor of 4395)
4395 / 2 = 2197.5 (the remainder is 1, so 2 is not a divisor of 4395)
4395 / 3 = 1465 (the remainder is 0, so 3 is a divisor of 4395)
...
4395 / 4394 = 1.0002275830678 (the remainder is 1, so 4394 is not a divisor of 4395)
4395 / 4395 = 1 (the remainder is 0, so 4395 is a divisor of 4395)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 4395 (i.e. 66.294796175869). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

4395 / 1 = 4395 (the remainder is 0, so 1 and 4395 are divisors of 4395)
4395 / 2 = 2197.5 (the remainder is 1, so 2 is not a divisor of 4395)
4395 / 3 = 1465 (the remainder is 0, so 3 and 1465 are divisors of 4395)
...
4395 / 65 = 67.615384615385 (the remainder is 40, so 65 is not a divisor of 4395)
4395 / 66 = 66.590909090909 (the remainder is 39, so 66 is not a divisor of 4395)