What are the divisors of 3196?

1, 2, 4, 17, 34, 47, 68, 94, 188, 799, 1598, 3196

There is a total of 12 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 504.

8 even divisors

2, 4, 34, 68, 94, 188, 1598, 3196

4 odd divisors

1, 17, 47, 799

How to compute the divisors of 3196?

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 3196 by each of the numbers from 1 to 3196 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)

3196 / 1 = 3196 (the remainder is 0, so 1 is a divisor of 3196)
3196 / 2 = 1598 (the remainder is 0, so 2 is a divisor of 3196)
3196 / 3 = 1065.3333333333 (the remainder is 1, so 3 is not a divisor of 3196)
...
3196 / 3195 = 1.0003129890454 (the remainder is 1, so 3195 is not a divisor of 3196)
3196 / 3196 = 1 (the remainder is 0, so 3196 is a divisor of 3196)

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 3196 (i.e. 56.53317610041). 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 $\frac{N}{d} = D$ )

3196 / 1 = 3196 (the remainder is 0, so 1 and 3196 are divisors of 3196)
3196 / 2 = 1598 (the remainder is 0, so 2 and 1598 are divisors of 3196)
3196 / 3 = 1065.3333333333 (the remainder is 1, so 3 is not a divisor of 3196)
...
3196 / 55 = 58.109090909091 (the remainder is 6, so 55 is not a divisor of 3196)
3196 / 56 = 57.071428571429 (the remainder is 4, so 56 is not a divisor of 3196)