What are the divisors of 3164?

1, 2, 4, 7, 14, 28, 113, 226, 452, 791, 1582, 3164

There is a total of 12 positive divisors.
The sum of these divisors is 6384.
The arithmetic mean is 532.

8 even divisors

2, 4, 14, 28, 226, 452, 1582, 3164

4 odd divisors

1, 7, 113, 791

How to compute the divisors of 3164?

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 3164 by each of the numbers from 1 to 3164 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)

3164 / 1 = 3164 (the remainder is 0, so 1 is a divisor of 3164)
3164 / 2 = 1582 (the remainder is 0, so 2 is a divisor of 3164)
3164 / 3 = 1054.6666666667 (the remainder is 2, so 3 is not a divisor of 3164)
...
3164 / 3163 = 1.0003161555485 (the remainder is 1, so 3163 is not a divisor of 3164)
3164 / 3164 = 1 (the remainder is 0, so 3164 is a divisor of 3164)

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 3164 (i.e. 56.249444441701). 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 $\frac{N}{d} = D$ )

3164 / 1 = 3164 (the remainder is 0, so 1 and 3164 are divisors of 3164)
3164 / 2 = 1582 (the remainder is 0, so 2 and 1582 are divisors of 3164)
3164 / 3 = 1054.6666666667 (the remainder is 2, so 3 is not a divisor of 3164)
...
3164 / 55 = 57.527272727273 (the remainder is 29, so 55 is not a divisor of 3164)
3164 / 56 = 56.5 (the remainder is 28, so 56 is not a divisor of 3164)