What are the divisors of 3425?

1, 5, 25, 137, 685, 3425

There is a total of 6 positive divisors.
The sum of these divisors is 4278.
The arithmetic mean is 713.

6 odd divisors

1, 5, 25, 137, 685, 3425

How to compute the divisors of 3425?

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 3425 by each of the numbers from 1 to 3425 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)

3425 / 1 = 3425 (the remainder is 0, so 1 is a divisor of 3425)
3425 / 2 = 1712.5 (the remainder is 1, so 2 is not a divisor of 3425)
3425 / 3 = 1141.6666666667 (the remainder is 2, so 3 is not a divisor of 3425)
...
3425 / 3424 = 1.0002920560748 (the remainder is 1, so 3424 is not a divisor of 3425)
3425 / 3425 = 1 (the remainder is 0, so 3425 is a divisor of 3425)

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 3425 (i.e. 58.523499553598). 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 $\frac{N}{d} = D$ )

3425 / 1 = 3425 (the remainder is 0, so 1 and 3425 are divisors of 3425)
3425 / 2 = 1712.5 (the remainder is 1, so 2 is not a divisor of 3425)
3425 / 3 = 1141.6666666667 (the remainder is 2, so 3 is not a divisor of 3425)
...
3425 / 57 = 60.087719298246 (the remainder is 5, so 57 is not a divisor of 3425)
3425 / 58 = 59.051724137931 (the remainder is 3, so 58 is not a divisor of 3425)