What are the divisors of 203?

1, 7, 29, 203

There is a total of 4 positive divisors.
The sum of these divisors is 240.
The arithmetic mean is 60.

4 odd divisors

1, 7, 29, 203

How to compute the divisors of 203?

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 203 by each of the numbers from 1 to 203 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)

203 / 1 = 203 (the remainder is 0, so 1 is a divisor of 203)
203 / 2 = 101.5 (the remainder is 1, so 2 is not a divisor of 203)
203 / 3 = 67.666666666667 (the remainder is 2, so 3 is not a divisor of 203)
...
203 / 202 = 1.0049504950495 (the remainder is 1, so 202 is not a divisor of 203)
203 / 203 = 1 (the remainder is 0, so 203 is a divisor of 203)

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 203 (i.e. 14.247806848775). 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 $\frac{N}{d} = D$ )

203 / 1 = 203 (the remainder is 0, so 1 and 203 are divisors of 203)
203 / 2 = 101.5 (the remainder is 1, so 2 is not a divisor of 203)
203 / 3 = 67.666666666667 (the remainder is 2, so 3 is not a divisor of 203)
...
203 / 13 = 15.615384615385 (the remainder is 8, so 13 is not a divisor of 203)
203 / 14 = 14.5 (the remainder is 7, so 14 is not a divisor of 203)