What are the divisors of 466?

1, 2, 233, 466

There is a total of 4 positive divisors.
The sum of these divisors is 702.
The arithmetic mean is 175.5.

2 even divisors

2, 466

2 odd divisors

1, 233

How to compute the divisors of 466?

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 466 by each of the numbers from 1 to 466 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)

466 / 1 = 466 (the remainder is 0, so 1 is a divisor of 466)
466 / 2 = 233 (the remainder is 0, so 2 is a divisor of 466)
466 / 3 = 155.33333333333 (the remainder is 1, so 3 is not a divisor of 466)
...
466 / 465 = 1.0021505376344 (the remainder is 1, so 465 is not a divisor of 466)
466 / 466 = 1 (the remainder is 0, so 466 is a divisor of 466)

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 466 (i.e. 21.587033144923). 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 $\frac{N}{d} = D$ )

466 / 1 = 466 (the remainder is 0, so 1 and 466 are divisors of 466)
466 / 2 = 233 (the remainder is 0, so 2 and 233 are divisors of 466)
466 / 3 = 155.33333333333 (the remainder is 1, so 3 is not a divisor of 466)
...
466 / 20 = 23.3 (the remainder is 6, so 20 is not a divisor of 466)
466 / 21 = 22.190476190476 (the remainder is 4, so 21 is not a divisor of 466)