What are the divisors of 494?

1, 2, 13, 19, 26, 38, 247, 494

There is a total of 8 positive divisors.
The sum of these divisors is 840.
The arithmetic mean is 105.

4 even divisors

2, 26, 38, 494

4 odd divisors

1, 13, 19, 247

How to compute the divisors of 494?

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 494 by each of the numbers from 1 to 494 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)

494 / 1 = 494 (the remainder is 0, so 1 is a divisor of 494)
494 / 2 = 247 (the remainder is 0, so 2 is a divisor of 494)
494 / 3 = 164.66666666667 (the remainder is 2, so 3 is not a divisor of 494)
...
494 / 493 = 1.0020283975659 (the remainder is 1, so 493 is not a divisor of 494)
494 / 494 = 1 (the remainder is 0, so 494 is a divisor of 494)

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 494 (i.e. 22.226110770893). 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 $\frac{N}{d} = D$ )

494 / 1 = 494 (the remainder is 0, so 1 and 494 are divisors of 494)
494 / 2 = 247 (the remainder is 0, so 2 and 247 are divisors of 494)
494 / 3 = 164.66666666667 (the remainder is 2, so 3 is not a divisor of 494)
...
494 / 21 = 23.52380952381 (the remainder is 11, so 21 is not a divisor of 494)
494 / 22 = 22.454545454545 (the remainder is 10, so 22 is not a divisor of 494)