What are the divisors of 3151?

1, 23, 137, 3151

There is a total of 4 positive divisors.
The sum of these divisors is 3312.
The arithmetic mean is 828.

4 odd divisors

1, 23, 137, 3151

How to compute the divisors of 3151?

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 3151 by each of the numbers from 1 to 3151 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)

3151 / 1 = 3151 (the remainder is 0, so 1 is a divisor of 3151)
3151 / 2 = 1575.5 (the remainder is 1, so 2 is not a divisor of 3151)
3151 / 3 = 1050.3333333333 (the remainder is 1, so 3 is not a divisor of 3151)
...
3151 / 3150 = 1.0003174603175 (the remainder is 1, so 3150 is not a divisor of 3151)
3151 / 3151 = 1 (the remainder is 0, so 3151 is a divisor of 3151)

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 3151 (i.e. 56.133768802745). 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 $\frac{N}{d} = D$ )

3151 / 1 = 3151 (the remainder is 0, so 1 and 3151 are divisors of 3151)
3151 / 2 = 1575.5 (the remainder is 1, so 2 is not a divisor of 3151)
3151 / 3 = 1050.3333333333 (the remainder is 1, so 3 is not a divisor of 3151)
...
3151 / 55 = 57.290909090909 (the remainder is 16, so 55 is not a divisor of 3151)
3151 / 56 = 56.267857142857 (the remainder is 15, so 56 is not a divisor of 3151)