What are the divisors of 458?

1, 2, 229, 458

There is a total of 4 positive divisors.
The sum of these divisors is 690.
The arithmetic mean is 172.5.

2 even divisors

2, 458

2 odd divisors

1, 229

How to compute the divisors of 458?

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 458 by each of the numbers from 1 to 458 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)

458 / 1 = 458 (the remainder is 0, so 1 is a divisor of 458)
458 / 2 = 229 (the remainder is 0, so 2 is a divisor of 458)
458 / 3 = 152.66666666667 (the remainder is 2, so 3 is not a divisor of 458)
...
458 / 457 = 1.0021881838074 (the remainder is 1, so 457 is not a divisor of 458)
458 / 458 = 1 (the remainder is 0, so 458 is a divisor of 458)

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 458 (i.e. 21.400934559033). 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 $\frac{N}{d} = D$ )

458 / 1 = 458 (the remainder is 0, so 1 and 458 are divisors of 458)
458 / 2 = 229 (the remainder is 0, so 2 and 229 are divisors of 458)
458 / 3 = 152.66666666667 (the remainder is 2, so 3 is not a divisor of 458)
...
458 / 20 = 22.9 (the remainder is 18, so 20 is not a divisor of 458)
458 / 21 = 21.809523809524 (the remainder is 17, so 21 is not a divisor of 458)