What are the divisors of 3435?

1, 3, 5, 15, 229, 687, 1145, 3435

There is a total of 8 positive divisors.
The sum of these divisors is 5520.
The arithmetic mean is 690.

8 odd divisors

1, 3, 5, 15, 229, 687, 1145, 3435

How to compute the divisors of 3435?

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 3435 by each of the numbers from 1 to 3435 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)

3435 / 1 = 3435 (the remainder is 0, so 1 is a divisor of 3435)
3435 / 2 = 1717.5 (the remainder is 1, so 2 is not a divisor of 3435)
3435 / 3 = 1145 (the remainder is 0, so 3 is a divisor of 3435)
...
3435 / 3434 = 1.0002912055911 (the remainder is 1, so 3434 is not a divisor of 3435)
3435 / 3435 = 1 (the remainder is 0, so 3435 is a divisor of 3435)

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 3435 (i.e. 58.60887304837). 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 $\frac{N}{d} = D$ )

3435 / 1 = 3435 (the remainder is 0, so 1 and 3435 are divisors of 3435)
3435 / 2 = 1717.5 (the remainder is 1, so 2 is not a divisor of 3435)
3435 / 3 = 1145 (the remainder is 0, so 3 and 1145 are divisors of 3435)
...
3435 / 57 = 60.263157894737 (the remainder is 15, so 57 is not a divisor of 3435)
3435 / 58 = 59.224137931034 (the remainder is 13, so 58 is not a divisor of 3435)