What are the divisors of 2454?

1, 2, 3, 6, 409, 818, 1227, 2454

There is a total of 8 positive divisors.
The sum of these divisors is 4920.
The arithmetic mean is 615.

4 even divisors

2, 6, 818, 2454

4 odd divisors

1, 3, 409, 1227

How to compute the divisors of 2454?

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 2454 by each of the numbers from 1 to 2454 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)

2454 / 1 = 2454 (the remainder is 0, so 1 is a divisor of 2454)
2454 / 2 = 1227 (the remainder is 0, so 2 is a divisor of 2454)
2454 / 3 = 818 (the remainder is 0, so 3 is a divisor of 2454)
...
2454 / 2453 = 1.0004076640848 (the remainder is 1, so 2453 is not a divisor of 2454)
2454 / 2454 = 1 (the remainder is 0, so 2454 is a divisor of 2454)

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 2454 (i.e. 49.537864306003). 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 $\frac{N}{d} = D$ )

2454 / 1 = 2454 (the remainder is 0, so 1 and 2454 are divisors of 2454)
2454 / 2 = 1227 (the remainder is 0, so 2 and 1227 are divisors of 2454)
2454 / 3 = 818 (the remainder is 0, so 3 and 818 are divisors of 2454)
...
2454 / 48 = 51.125 (the remainder is 6, so 48 is not a divisor of 2454)
2454 / 49 = 50.081632653061 (the remainder is 4, so 49 is not a divisor of 2454)