What are the divisors of 3355?

1, 5, 11, 55, 61, 305, 671, 3355

There is a total of 8 positive divisors.
The sum of these divisors is 4464.
The arithmetic mean is 558.

8 odd divisors

1, 5, 11, 55, 61, 305, 671, 3355

How to compute the divisors of 3355?

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 3355 by each of the numbers from 1 to 3355 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)

3355 / 1 = 3355 (the remainder is 0, so 1 is a divisor of 3355)
3355 / 2 = 1677.5 (the remainder is 1, so 2 is not a divisor of 3355)
3355 / 3 = 1118.3333333333 (the remainder is 1, so 3 is not a divisor of 3355)
...
3355 / 3354 = 1.0002981514609 (the remainder is 1, so 3354 is not a divisor of 3355)
3355 / 3355 = 1 (the remainder is 0, so 3355 is a divisor of 3355)

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 3355 (i.e. 57.922361830298). 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 $\frac{N}{d} = D$ )

3355 / 1 = 3355 (the remainder is 0, so 1 and 3355 are divisors of 3355)
3355 / 2 = 1677.5 (the remainder is 1, so 2 is not a divisor of 3355)
3355 / 3 = 1118.3333333333 (the remainder is 1, so 3 is not a divisor of 3355)
...
3355 / 56 = 59.910714285714 (the remainder is 51, so 56 is not a divisor of 3355)
3355 / 57 = 58.859649122807 (the remainder is 49, so 57 is not a divisor of 3355)