What are the divisors of 3101?

1, 7, 443, 3101

There is a total of 4 positive divisors.
The sum of these divisors is 3552.
The arithmetic mean is 888.

4 odd divisors

1, 7, 443, 3101

How to compute the divisors of 3101?

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 3101 by each of the numbers from 1 to 3101 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)

3101 / 1 = 3101 (the remainder is 0, so 1 is a divisor of 3101)
3101 / 2 = 1550.5 (the remainder is 1, so 2 is not a divisor of 3101)
3101 / 3 = 1033.6666666667 (the remainder is 2, so 3 is not a divisor of 3101)
...
3101 / 3100 = 1.0003225806452 (the remainder is 1, so 3100 is not a divisor of 3101)
3101 / 3101 = 1 (the remainder is 0, so 3101 is a divisor of 3101)

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 3101 (i.e. 55.686623169303). 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 $\frac{N}{d} = D$ )

3101 / 1 = 3101 (the remainder is 0, so 1 and 3101 are divisors of 3101)
3101 / 2 = 1550.5 (the remainder is 1, so 2 is not a divisor of 3101)
3101 / 3 = 1033.6666666667 (the remainder is 2, so 3 is not a divisor of 3101)
...
3101 / 54 = 57.425925925926 (the remainder is 23, so 54 is not a divisor of 3101)
3101 / 55 = 56.381818181818 (the remainder is 21, so 55 is not a divisor of 3101)