What are the divisors of 2456?

1, 2, 4, 8, 307, 614, 1228, 2456

There is a total of 8 positive divisors.
The sum of these divisors is 4620.
The arithmetic mean is 577.5.

6 even divisors

2, 4, 8, 614, 1228, 2456

2 odd divisors

1, 307

How to compute the divisors of 2456?

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 2456 by each of the numbers from 1 to 2456 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)

2456 / 1 = 2456 (the remainder is 0, so 1 is a divisor of 2456)
2456 / 2 = 1228 (the remainder is 0, so 2 is a divisor of 2456)
2456 / 3 = 818.66666666667 (the remainder is 2, so 3 is not a divisor of 2456)
...
2456 / 2455 = 1.0004073319756 (the remainder is 1, so 2455 is not a divisor of 2456)
2456 / 2456 = 1 (the remainder is 0, so 2456 is a divisor of 2456)

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 2456 (i.e. 49.558046773455). 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 $\frac{N}{d} = D$ )

2456 / 1 = 2456 (the remainder is 0, so 1 and 2456 are divisors of 2456)
2456 / 2 = 1228 (the remainder is 0, so 2 and 1228 are divisors of 2456)
2456 / 3 = 818.66666666667 (the remainder is 2, so 3 is not a divisor of 2456)
...
2456 / 48 = 51.166666666667 (the remainder is 8, so 48 is not a divisor of 2456)
2456 / 49 = 50.122448979592 (the remainder is 6, so 49 is not a divisor of 2456)