What are the divisors of 3395?

1, 5, 7, 35, 97, 485, 679, 3395

There is a total of 8 positive divisors.
The sum of these divisors is 4704.
The arithmetic mean is 588.

8 odd divisors

1, 5, 7, 35, 97, 485, 679, 3395

How to compute the divisors of 3395?

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 3395 by each of the numbers from 1 to 3395 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)

3395 / 1 = 3395 (the remainder is 0, so 1 is a divisor of 3395)
3395 / 2 = 1697.5 (the remainder is 1, so 2 is not a divisor of 3395)
3395 / 3 = 1131.6666666667 (the remainder is 2, so 3 is not a divisor of 3395)
...
3395 / 3394 = 1.0002946375958 (the remainder is 1, so 3394 is not a divisor of 3395)
3395 / 3395 = 1 (the remainder is 0, so 3395 is a divisor of 3395)

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 3395 (i.e. 58.266628527829). 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 $\frac{N}{d} = D$ )

3395 / 1 = 3395 (the remainder is 0, so 1 and 3395 are divisors of 3395)
3395 / 2 = 1697.5 (the remainder is 1, so 2 is not a divisor of 3395)
3395 / 3 = 1131.6666666667 (the remainder is 2, so 3 is not a divisor of 3395)
...
3395 / 57 = 59.561403508772 (the remainder is 32, so 57 is not a divisor of 3395)
3395 / 58 = 58.534482758621 (the remainder is 31, so 58 is not a divisor of 3395)