What are the divisors of 363?

1, 3, 11, 33, 121, 363

There is a total of 6 positive divisors.
The sum of these divisors is 532.
The arithmetic mean is 88.666666666667.

6 odd divisors

1, 3, 11, 33, 121, 363

How to compute the divisors of 363?

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 363 by each of the numbers from 1 to 363 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)

363 / 1 = 363 (the remainder is 0, so 1 is a divisor of 363)
363 / 2 = 181.5 (the remainder is 1, so 2 is not a divisor of 363)
363 / 3 = 121 (the remainder is 0, so 3 is a divisor of 363)
...
363 / 362 = 1.0027624309392 (the remainder is 1, so 362 is not a divisor of 363)
363 / 363 = 1 (the remainder is 0, so 363 is a divisor of 363)

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 363 (i.e. 19.052558883258). 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 $\frac{N}{d} = D$ )

363 / 1 = 363 (the remainder is 0, so 1 and 363 are divisors of 363)
363 / 2 = 181.5 (the remainder is 1, so 2 is not a divisor of 363)
363 / 3 = 121 (the remainder is 0, so 3 and 121 are divisors of 363)
...
363 / 18 = 20.166666666667 (the remainder is 3, so 18 is not a divisor of 363)
363 / 19 = 19.105263157895 (the remainder is 2, so 19 is not a divisor of 363)