What are the divisors of 2410?

1, 2, 5, 10, 241, 482, 1205, 2410

There is a total of 8 positive divisors.
The sum of these divisors is 4356.
The arithmetic mean is 544.5.

4 even divisors

2, 10, 482, 2410

4 odd divisors

1, 5, 241, 1205

How to compute the divisors of 2410?

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 2410 by each of the numbers from 1 to 2410 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)

2410 / 1 = 2410 (the remainder is 0, so 1 is a divisor of 2410)
2410 / 2 = 1205 (the remainder is 0, so 2 is a divisor of 2410)
2410 / 3 = 803.33333333333 (the remainder is 1, so 3 is not a divisor of 2410)
...
2410 / 2409 = 1.0004151100042 (the remainder is 1, so 2409 is not a divisor of 2410)
2410 / 2410 = 1 (the remainder is 0, so 2410 is a divisor of 2410)

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 2410 (i.e. 49.091750834534). 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 $\frac{N}{d} = D$ )

2410 / 1 = 2410 (the remainder is 0, so 1 and 2410 are divisors of 2410)
2410 / 2 = 1205 (the remainder is 0, so 2 and 1205 are divisors of 2410)
2410 / 3 = 803.33333333333 (the remainder is 1, so 3 is not a divisor of 2410)
...
2410 / 48 = 50.208333333333 (the remainder is 10, so 48 is not a divisor of 2410)
2410 / 49 = 49.183673469388 (the remainder is 9, so 49 is not a divisor of 2410)