What are the divisors of 482?

1, 2, 241, 482

There is a total of 4 positive divisors.
The sum of these divisors is 726.
The arithmetic mean is 181.5.

2 even divisors

2, 482

2 odd divisors

1, 241

How to compute the divisors of 482?

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 482 by each of the numbers from 1 to 482 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)

482 / 1 = 482 (the remainder is 0, so 1 is a divisor of 482)
482 / 2 = 241 (the remainder is 0, so 2 is a divisor of 482)
482 / 3 = 160.66666666667 (the remainder is 2, so 3 is not a divisor of 482)
...
482 / 481 = 1.002079002079 (the remainder is 1, so 481 is not a divisor of 482)
482 / 482 = 1 (the remainder is 0, so 482 is a divisor of 482)

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 482 (i.e. 21.9544984001). 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 $\frac{N}{d} = D$ )

482 / 1 = 482 (the remainder is 0, so 1 and 482 are divisors of 482)
482 / 2 = 241 (the remainder is 0, so 2 and 241 are divisors of 482)
482 / 3 = 160.66666666667 (the remainder is 2, so 3 is not a divisor of 482)
...
482 / 20 = 24.1 (the remainder is 2, so 20 is not a divisor of 482)
482 / 21 = 22.952380952381 (the remainder is 20, so 21 is not a divisor of 482)