What are the divisors of 464?

1, 2, 4, 8, 16, 29, 58, 116, 232, 464

There is a total of 10 positive divisors.
The sum of these divisors is 930.
The arithmetic mean is 93.

8 even divisors

2, 4, 8, 16, 58, 116, 232, 464

2 odd divisors

1, 29

How to compute the divisors of 464?

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 464 by each of the numbers from 1 to 464 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)

464 / 1 = 464 (the remainder is 0, so 1 is a divisor of 464)
464 / 2 = 232 (the remainder is 0, so 2 is a divisor of 464)
464 / 3 = 154.66666666667 (the remainder is 2, so 3 is not a divisor of 464)
...
464 / 463 = 1.0021598272138 (the remainder is 1, so 463 is not a divisor of 464)
464 / 464 = 1 (the remainder is 0, so 464 is a divisor of 464)

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 464 (i.e. 21.540659228538). 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 $\frac{N}{d} = D$ )

464 / 1 = 464 (the remainder is 0, so 1 and 464 are divisors of 464)
464 / 2 = 232 (the remainder is 0, so 2 and 232 are divisors of 464)
464 / 3 = 154.66666666667 (the remainder is 2, so 3 is not a divisor of 464)
...
464 / 20 = 23.2 (the remainder is 4, so 20 is not a divisor of 464)
464 / 21 = 22.095238095238 (the remainder is 2, so 21 is not a divisor of 464)