What are the divisors of 493?

1, 17, 29, 493

There is a total of 4 positive divisors.
The sum of these divisors is 540.
The arithmetic mean is 135.

4 odd divisors

1, 17, 29, 493

How to compute the divisors of 493?

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 493 by each of the numbers from 1 to 493 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)

493 / 1 = 493 (the remainder is 0, so 1 is a divisor of 493)
493 / 2 = 246.5 (the remainder is 1, so 2 is not a divisor of 493)
493 / 3 = 164.33333333333 (the remainder is 1, so 3 is not a divisor of 493)
...
493 / 492 = 1.0020325203252 (the remainder is 1, so 492 is not a divisor of 493)
493 / 493 = 1 (the remainder is 0, so 493 is a divisor of 493)

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 493 (i.e. 22.203603311175). 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 $\frac{N}{d} = D$ )

493 / 1 = 493 (the remainder is 0, so 1 and 493 are divisors of 493)
493 / 2 = 246.5 (the remainder is 1, so 2 is not a divisor of 493)
493 / 3 = 164.33333333333 (the remainder is 1, so 3 is not a divisor of 493)
...
493 / 21 = 23.47619047619 (the remainder is 10, so 21 is not a divisor of 493)
493 / 22 = 22.409090909091 (the remainder is 9, so 22 is not a divisor of 493)