What are the divisors of 2315?

1, 5, 463, 2315

There is a total of 4 positive divisors.
The sum of these divisors is 2784.
The arithmetic mean is 696.

4 odd divisors

1, 5, 463, 2315

How to compute the divisors of 2315?

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 2315 by each of the numbers from 1 to 2315 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)

2315 / 1 = 2315 (the remainder is 0, so 1 is a divisor of 2315)
2315 / 2 = 1157.5 (the remainder is 1, so 2 is not a divisor of 2315)
2315 / 3 = 771.66666666667 (the remainder is 2, so 3 is not a divisor of 2315)
...
2315 / 2314 = 1.0004321521175 (the remainder is 1, so 2314 is not a divisor of 2315)
2315 / 2315 = 1 (the remainder is 0, so 2315 is a divisor of 2315)

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 2315 (i.e. 48.114446894878). 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 $\frac{N}{d} = D$ )

2315 / 1 = 2315 (the remainder is 0, so 1 and 2315 are divisors of 2315)
2315 / 2 = 1157.5 (the remainder is 1, so 2 is not a divisor of 2315)
2315 / 3 = 771.66666666667 (the remainder is 2, so 3 is not a divisor of 2315)
...
2315 / 47 = 49.255319148936 (the remainder is 12, so 47 is not a divisor of 2315)
2315 / 48 = 48.229166666667 (the remainder is 11, so 48 is not a divisor of 2315)