What are the divisors of 4011?

1, 3, 7, 21, 191, 573, 1337, 4011

There is a total of 8 positive divisors.
The sum of these divisors is 6144.
The arithmetic mean is 768.

8 odd divisors

1, 3, 7, 21, 191, 573, 1337, 4011

How to compute the divisors of 4011?

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 4011 by each of the numbers from 1 to 4011 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)

4011 / 1 = 4011 (the remainder is 0, so 1 is a divisor of 4011)
4011 / 2 = 2005.5 (the remainder is 1, so 2 is not a divisor of 4011)
4011 / 3 = 1337 (the remainder is 0, so 3 is a divisor of 4011)
...
4011 / 4010 = 1.0002493765586 (the remainder is 1, so 4010 is not a divisor of 4011)
4011 / 4011 = 1 (the remainder is 0, so 4011 is a divisor of 4011)

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 4011 (i.e. 63.332456134276). 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 $\frac{N}{d} = D$ )

4011 / 1 = 4011 (the remainder is 0, so 1 and 4011 are divisors of 4011)
4011 / 2 = 2005.5 (the remainder is 1, so 2 is not a divisor of 4011)
4011 / 3 = 1337 (the remainder is 0, so 3 and 1337 are divisors of 4011)
...
4011 / 62 = 64.693548387097 (the remainder is 43, so 62 is not a divisor of 4011)
4011 / 63 = 63.666666666667 (the remainder is 42, so 63 is not a divisor of 4011)