What are the divisors of 3175?

1, 5, 25, 127, 635, 3175

There is a total of 6 positive divisors.
The sum of these divisors is 3968.
The arithmetic mean is 661.33333333333.

6 odd divisors

1, 5, 25, 127, 635, 3175

How to compute the divisors of 3175?

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 3175 by each of the numbers from 1 to 3175 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)

3175 / 1 = 3175 (the remainder is 0, so 1 is a divisor of 3175)
3175 / 2 = 1587.5 (the remainder is 1, so 2 is not a divisor of 3175)
3175 / 3 = 1058.3333333333 (the remainder is 1, so 3 is not a divisor of 3175)
...
3175 / 3174 = 1.0003150598614 (the remainder is 1, so 3174 is not a divisor of 3175)
3175 / 3175 = 1 (the remainder is 0, so 3175 is a divisor of 3175)

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 3175 (i.e. 56.347138347923). 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 $\frac{N}{d} = D$ )

3175 / 1 = 3175 (the remainder is 0, so 1 and 3175 are divisors of 3175)
3175 / 2 = 1587.5 (the remainder is 1, so 2 is not a divisor of 3175)
3175 / 3 = 1058.3333333333 (the remainder is 1, so 3 is not a divisor of 3175)
...
3175 / 55 = 57.727272727273 (the remainder is 40, so 55 is not a divisor of 3175)
3175 / 56 = 56.696428571429 (the remainder is 39, so 56 is not a divisor of 3175)