What are the divisors of 1205?

1, 5, 241, 1205

There is a total of 4 positive divisors.
The sum of these divisors is 1452.
The arithmetic mean is 363.

4 odd divisors

1, 5, 241, 1205

How to compute the divisors of 1205?

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 1205 by each of the numbers from 1 to 1205 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)

1205 / 1 = 1205 (the remainder is 0, so 1 is a divisor of 1205)
1205 / 2 = 602.5 (the remainder is 1, so 2 is not a divisor of 1205)
1205 / 3 = 401.66666666667 (the remainder is 2, so 3 is not a divisor of 1205)
...
1205 / 1204 = 1.0008305647841 (the remainder is 1, so 1204 is not a divisor of 1205)
1205 / 1205 = 1 (the remainder is 0, so 1205 is a divisor of 1205)

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 1205 (i.e. 34.71310991542). 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 $\frac{N}{d} = D$ )

1205 / 1 = 1205 (the remainder is 0, so 1 and 1205 are divisors of 1205)
1205 / 2 = 602.5 (the remainder is 1, so 2 is not a divisor of 1205)
1205 / 3 = 401.66666666667 (the remainder is 2, so 3 is not a divisor of 1205)
...
1205 / 33 = 36.515151515152 (the remainder is 17, so 33 is not a divisor of 1205)
1205 / 34 = 35.441176470588 (the remainder is 15, so 34 is not a divisor of 1205)