What are the divisors of 2455?

1, 5, 491, 2455

There is a total of 4 positive divisors.
The sum of these divisors is 2952.
The arithmetic mean is 738.

4 odd divisors

1, 5, 491, 2455

How to compute the divisors of 2455?

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 2455 by each of the numbers from 1 to 2455 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)

2455 / 1 = 2455 (the remainder is 0, so 1 is a divisor of 2455)
2455 / 2 = 1227.5 (the remainder is 1, so 2 is not a divisor of 2455)
2455 / 3 = 818.33333333333 (the remainder is 1, so 3 is not a divisor of 2455)
...
2455 / 2454 = 1.0004074979625 (the remainder is 1, so 2454 is not a divisor of 2455)
2455 / 2455 = 1 (the remainder is 0, so 2455 is a divisor of 2455)

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 2455 (i.e. 49.54795656735). 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 $\frac{N}{d} = D$ )

2455 / 1 = 2455 (the remainder is 0, so 1 and 2455 are divisors of 2455)
2455 / 2 = 1227.5 (the remainder is 1, so 2 is not a divisor of 2455)
2455 / 3 = 818.33333333333 (the remainder is 1, so 3 is not a divisor of 2455)
...
2455 / 48 = 51.145833333333 (the remainder is 7, so 48 is not a divisor of 2455)
2455 / 49 = 50.102040816327 (the remainder is 5, so 49 is not a divisor of 2455)