What are the divisors of 4010?

1, 2, 5, 10, 401, 802, 2005, 4010

There is a total of 8 positive divisors.
The sum of these divisors is 7236.
The arithmetic mean is 904.5.

4 even divisors

2, 10, 802, 4010

4 odd divisors

1, 5, 401, 2005

How to compute the divisors of 4010?

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 4010 by each of the numbers from 1 to 4010 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)

4010 / 1 = 4010 (the remainder is 0, so 1 is a divisor of 4010)
4010 / 2 = 2005 (the remainder is 0, so 2 is a divisor of 4010)
4010 / 3 = 1336.6666666667 (the remainder is 2, so 3 is not a divisor of 4010)
...
4010 / 4009 = 1.0002494387628 (the remainder is 1, so 4009 is not a divisor of 4010)
4010 / 4010 = 1 (the remainder is 0, so 4010 is a divisor of 4010)

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 4010 (i.e. 63.32456079595). 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 $\frac{N}{d} = D$ )

4010 / 1 = 4010 (the remainder is 0, so 1 and 4010 are divisors of 4010)
4010 / 2 = 2005 (the remainder is 0, so 2 and 2005 are divisors of 4010)
4010 / 3 = 1336.6666666667 (the remainder is 2, so 3 is not a divisor of 4010)
...
4010 / 62 = 64.677419354839 (the remainder is 42, so 62 is not a divisor of 4010)
4010 / 63 = 63.650793650794 (the remainder is 41, so 63 is not a divisor of 4010)