What are the divisors of 3174?

1, 2, 3, 6, 23, 46, 69, 138, 529, 1058, 1587, 3174

There is a total of 12 positive divisors.
The sum of these divisors is 6636.
The arithmetic mean is 553.

6 even divisors

2, 6, 46, 138, 1058, 3174

6 odd divisors

1, 3, 23, 69, 529, 1587

How to compute the divisors of 3174?

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 3174 by each of the numbers from 1 to 3174 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)

3174 / 1 = 3174 (the remainder is 0, so 1 is a divisor of 3174)
3174 / 2 = 1587 (the remainder is 0, so 2 is a divisor of 3174)
3174 / 3 = 1058 (the remainder is 0, so 3 is a divisor of 3174)
...
3174 / 3173 = 1.0003151591554 (the remainder is 1, so 3173 is not a divisor of 3174)
3174 / 3174 = 1 (the remainder is 0, so 3174 is a divisor of 3174)

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 3174 (i.e. 56.338264084013). 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 $\frac{N}{d} = D$ )

3174 / 1 = 3174 (the remainder is 0, so 1 and 3174 are divisors of 3174)
3174 / 2 = 1587 (the remainder is 0, so 2 and 1587 are divisors of 3174)
3174 / 3 = 1058 (the remainder is 0, so 3 and 1058 are divisors of 3174)
...
3174 / 55 = 57.709090909091 (the remainder is 39, so 55 is not a divisor of 3174)
3174 / 56 = 56.678571428571 (the remainder is 38, so 56 is not a divisor of 3174)