What are the divisors of 3172?

1, 2, 4, 13, 26, 52, 61, 122, 244, 793, 1586, 3172

There is a total of 12 positive divisors.
The sum of these divisors is 6076.
The arithmetic mean is 506.33333333333.

8 even divisors

2, 4, 26, 52, 122, 244, 1586, 3172

4 odd divisors

1, 13, 61, 793

How to compute the divisors of 3172?

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 3172 by each of the numbers from 1 to 3172 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)

3172 / 1 = 3172 (the remainder is 0, so 1 is a divisor of 3172)
3172 / 2 = 1586 (the remainder is 0, so 2 is a divisor of 3172)
3172 / 3 = 1057.3333333333 (the remainder is 1, so 3 is not a divisor of 3172)
...
3172 / 3171 = 1.0003153579313 (the remainder is 1, so 3171 is not a divisor of 3172)
3172 / 3172 = 1 (the remainder is 0, so 3172 is a divisor of 3172)

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 3172 (i.e. 56.320511361315). 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 $\frac{N}{d} = D$ )

3172 / 1 = 3172 (the remainder is 0, so 1 and 3172 are divisors of 3172)
3172 / 2 = 1586 (the remainder is 0, so 2 and 1586 are divisors of 3172)
3172 / 3 = 1057.3333333333 (the remainder is 1, so 3 is not a divisor of 3172)
...
3172 / 55 = 57.672727272727 (the remainder is 37, so 55 is not a divisor of 3172)
3172 / 56 = 56.642857142857 (the remainder is 36, so 56 is not a divisor of 3172)