What are the divisors of 1355?

1, 5, 271, 1355

There is a total of 4 positive divisors.
The sum of these divisors is 1632.
The arithmetic mean is 408.

4 odd divisors

1, 5, 271, 1355

How to compute the divisors of 1355?

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 1355 by each of the numbers from 1 to 1355 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)

1355 / 1 = 1355 (the remainder is 0, so 1 is a divisor of 1355)
1355 / 2 = 677.5 (the remainder is 1, so 2 is not a divisor of 1355)
1355 / 3 = 451.66666666667 (the remainder is 2, so 3 is not a divisor of 1355)
...
1355 / 1354 = 1.0007385524372 (the remainder is 1, so 1354 is not a divisor of 1355)
1355 / 1355 = 1 (the remainder is 0, so 1355 is a divisor of 1355)

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 1355 (i.e. 36.810324638612). 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 $\frac{N}{d} = D$ )

1355 / 1 = 1355 (the remainder is 0, so 1 and 1355 are divisors of 1355)
1355 / 2 = 677.5 (the remainder is 1, so 2 is not a divisor of 1355)
1355 / 3 = 451.66666666667 (the remainder is 2, so 3 is not a divisor of 1355)
...
1355 / 35 = 38.714285714286 (the remainder is 25, so 35 is not a divisor of 1355)
1355 / 36 = 37.638888888889 (the remainder is 23, so 36 is not a divisor of 1355)