What are the divisors of 3127?

1, 53, 59, 3127

There is a total of 4 positive divisors.
The sum of these divisors is 3240.
The arithmetic mean is 810.

4 odd divisors

1, 53, 59, 3127

How to compute the divisors of 3127?

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 3127 by each of the numbers from 1 to 3127 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)

3127 / 1 = 3127 (the remainder is 0, so 1 is a divisor of 3127)
3127 / 2 = 1563.5 (the remainder is 1, so 2 is not a divisor of 3127)
3127 / 3 = 1042.3333333333 (the remainder is 1, so 3 is not a divisor of 3127)
...
3127 / 3126 = 1.0003198976328 (the remainder is 1, so 3126 is not a divisor of 3127)
3127 / 3127 = 1 (the remainder is 0, so 3127 is a divisor of 3127)

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 3127 (i.e. 55.919585120063). 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 $\frac{N}{d} = D$ )

3127 / 1 = 3127 (the remainder is 0, so 1 and 3127 are divisors of 3127)
3127 / 2 = 1563.5 (the remainder is 1, so 2 is not a divisor of 3127)
3127 / 3 = 1042.3333333333 (the remainder is 1, so 3 is not a divisor of 3127)
...
3127 / 54 = 57.907407407407 (the remainder is 49, so 54 is not a divisor of 3127)
3127 / 55 = 56.854545454545 (the remainder is 47, so 55 is not a divisor of 3127)