What are the divisors of 3171?

1, 3, 7, 21, 151, 453, 1057, 3171

There is a total of 8 positive divisors.
The sum of these divisors is 4864.
The arithmetic mean is 608.

8 odd divisors

1, 3, 7, 21, 151, 453, 1057, 3171

How to compute the divisors of 3171?

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 3171 by each of the numbers from 1 to 3171 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)

3171 / 1 = 3171 (the remainder is 0, so 1 is a divisor of 3171)
3171 / 2 = 1585.5 (the remainder is 1, so 2 is not a divisor of 3171)
3171 / 3 = 1057 (the remainder is 0, so 3 is a divisor of 3171)
...
3171 / 3170 = 1.0003154574132 (the remainder is 1, so 3170 is not a divisor of 3171)
3171 / 3171 = 1 (the remainder is 0, so 3171 is a divisor of 3171)

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 3171 (i.e. 56.311632901204). 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 $\frac{N}{d} = D$ )

3171 / 1 = 3171 (the remainder is 0, so 1 and 3171 are divisors of 3171)
3171 / 2 = 1585.5 (the remainder is 1, so 2 is not a divisor of 3171)
3171 / 3 = 1057 (the remainder is 0, so 3 and 1057 are divisors of 3171)
...
3171 / 55 = 57.654545454545 (the remainder is 36, so 55 is not a divisor of 3171)
3171 / 56 = 56.625 (the remainder is 35, so 56 is not a divisor of 3171)