What are the divisors of 2458?

1, 2, 1229, 2458

There is a total of 4 positive divisors.
The sum of these divisors is 3690.
The arithmetic mean is 922.5.

2 even divisors

2, 2458

2 odd divisors

1, 1229

How to compute the divisors of 2458?

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 2458 by each of the numbers from 1 to 2458 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)

2458 / 1 = 2458 (the remainder is 0, so 1 is a divisor of 2458)
2458 / 2 = 1229 (the remainder is 0, so 2 is a divisor of 2458)
2458 / 3 = 819.33333333333 (the remainder is 1, so 3 is not a divisor of 2458)
...
2458 / 2457 = 1.000407000407 (the remainder is 1, so 2457 is not a divisor of 2458)
2458 / 2458 = 1 (the remainder is 0, so 2458 is a divisor of 2458)

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 2458 (i.e. 49.578221024962). 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 $\frac{N}{d} = D$ )

2458 / 1 = 2458 (the remainder is 0, so 1 and 2458 are divisors of 2458)
2458 / 2 = 1229 (the remainder is 0, so 2 and 1229 are divisors of 2458)
2458 / 3 = 819.33333333333 (the remainder is 1, so 3 is not a divisor of 2458)
...
2458 / 48 = 51.208333333333 (the remainder is 10, so 48 is not a divisor of 2458)
2458 / 49 = 50.163265306122 (the remainder is 8, so 49 is not a divisor of 2458)