What are the divisors of 2615?

1, 5, 523, 2615

There is a total of 4 positive divisors.
The sum of these divisors is 3144.
The arithmetic mean is 786.

4 odd divisors

1, 5, 523, 2615

How to compute the divisors of 2615?

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 2615 by each of the numbers from 1 to 2615 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)

2615 / 1 = 2615 (the remainder is 0, so 1 is a divisor of 2615)
2615 / 2 = 1307.5 (the remainder is 1, so 2 is not a divisor of 2615)
2615 / 3 = 871.66666666667 (the remainder is 2, so 3 is not a divisor of 2615)
...
2615 / 2614 = 1.0003825554705 (the remainder is 1, so 2614 is not a divisor of 2615)
2615 / 2615 = 1 (the remainder is 0, so 2615 is a divisor of 2615)

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 2615 (i.e. 51.137070702182). 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 $\frac{N}{d} = D$ )

2615 / 1 = 2615 (the remainder is 0, so 1 and 2615 are divisors of 2615)
2615 / 2 = 1307.5 (the remainder is 1, so 2 is not a divisor of 2615)
2615 / 3 = 871.66666666667 (the remainder is 2, so 3 is not a divisor of 2615)
...
2615 / 50 = 52.3 (the remainder is 15, so 50 is not a divisor of 2615)
2615 / 51 = 51.274509803922 (the remainder is 14, so 51 is not a divisor of 2615)