What are the divisors of 491?

1, 491

There is a total of 2 positive divisors.
The sum of these divisors is 492.
The arithmetic mean is 246.

2 odd divisors

1, 491

How to compute the divisors of 491?

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 491 by each of the numbers from 1 to 491 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)

491 / 1 = 491 (the remainder is 0, so 1 is a divisor of 491)
491 / 2 = 245.5 (the remainder is 1, so 2 is not a divisor of 491)
491 / 3 = 163.66666666667 (the remainder is 2, so 3 is not a divisor of 491)
...
491 / 490 = 1.0020408163265 (the remainder is 1, so 490 is not a divisor of 491)
491 / 491 = 1 (the remainder is 0, so 491 is a divisor of 491)

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 491 (i.e. 22.15851980616). 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 $\frac{N}{d} = D$ )

491 / 1 = 491 (the remainder is 0, so 1 and 491 are divisors of 491)
491 / 2 = 245.5 (the remainder is 1, so 2 is not a divisor of 491)
491 / 3 = 163.66666666667 (the remainder is 2, so 3 is not a divisor of 491)
...
491 / 21 = 23.380952380952 (the remainder is 8, so 21 is not a divisor of 491)
491 / 22 = 22.318181818182 (the remainder is 7, so 22 is not a divisor of 491)