What are the divisors of 3160?

1, 2, 4, 5, 8, 10, 20, 40, 79, 158, 316, 395, 632, 790, 1580, 3160

There is a total of 16 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 450.

12 even divisors

2, 4, 8, 10, 20, 40, 158, 316, 632, 790, 1580, 3160

4 odd divisors

1, 5, 79, 395

How to compute the divisors of 3160?

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 3160 by each of the numbers from 1 to 3160 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)

3160 / 1 = 3160 (the remainder is 0, so 1 is a divisor of 3160)
3160 / 2 = 1580 (the remainder is 0, so 2 is a divisor of 3160)
3160 / 3 = 1053.3333333333 (the remainder is 1, so 3 is not a divisor of 3160)
...
3160 / 3159 = 1.0003165558721 (the remainder is 1, so 3159 is not a divisor of 3160)
3160 / 3160 = 1 (the remainder is 0, so 3160 is a divisor of 3160)

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 3160 (i.e. 56.213877290221). 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 $\frac{N}{d} = D$ )

3160 / 1 = 3160 (the remainder is 0, so 1 and 3160 are divisors of 3160)
3160 / 2 = 1580 (the remainder is 0, so 2 and 1580 are divisors of 3160)
3160 / 3 = 1053.3333333333 (the remainder is 1, so 3 is not a divisor of 3160)
...
3160 / 55 = 57.454545454545 (the remainder is 25, so 55 is not a divisor of 3160)
3160 / 56 = 56.428571428571 (the remainder is 24, so 56 is not a divisor of 3160)