What are the divisors of 3455?

1, 5, 691, 3455

There is a total of 4 positive divisors.
The sum of these divisors is 4152.
The arithmetic mean is 1038.

4 odd divisors

1, 5, 691, 3455

How to compute the divisors of 3455?

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 3455 by each of the numbers from 1 to 3455 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)

3455 / 1 = 3455 (the remainder is 0, so 1 is a divisor of 3455)
3455 / 2 = 1727.5 (the remainder is 1, so 2 is not a divisor of 3455)
3455 / 3 = 1151.6666666667 (the remainder is 2, so 3 is not a divisor of 3455)
...
3455 / 3454 = 1.0002895193978 (the remainder is 1, so 3454 is not a divisor of 3455)
3455 / 3455 = 1 (the remainder is 0, so 3455 is a divisor of 3455)

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 3455 (i.e. 58.779248038742). 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 $\frac{N}{d} = D$ )

3455 / 1 = 3455 (the remainder is 0, so 1 and 3455 are divisors of 3455)
3455 / 2 = 1727.5 (the remainder is 1, so 2 is not a divisor of 3455)
3455 / 3 = 1151.6666666667 (the remainder is 2, so 3 is not a divisor of 3455)
...
3455 / 57 = 60.614035087719 (the remainder is 35, so 57 is not a divisor of 3455)
3455 / 58 = 59.568965517241 (the remainder is 33, so 58 is not a divisor of 3455)