What are the divisors of 4042?

1, 2, 43, 47, 86, 94, 2021, 4042

There is a total of 8 positive divisors.
The sum of these divisors is 6336.
The arithmetic mean is 792.

4 even divisors

2, 86, 94, 4042

4 odd divisors

1, 43, 47, 2021

How to compute the divisors of 4042?

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 4042 by each of the numbers from 1 to 4042 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)

4042 / 1 = 4042 (the remainder is 0, so 1 is a divisor of 4042)
4042 / 2 = 2021 (the remainder is 0, so 2 is a divisor of 4042)
4042 / 3 = 1347.3333333333 (the remainder is 1, so 3 is not a divisor of 4042)
...
4042 / 4041 = 1.0002474634991 (the remainder is 1, so 4041 is not a divisor of 4042)
4042 / 4042 = 1 (the remainder is 0, so 4042 is a divisor of 4042)

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 4042 (i.e. 63.576725301009). 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 $\frac{N}{d} = D$ )

4042 / 1 = 4042 (the remainder is 0, so 1 and 4042 are divisors of 4042)
4042 / 2 = 2021 (the remainder is 0, so 2 and 2021 are divisors of 4042)
4042 / 3 = 1347.3333333333 (the remainder is 1, so 3 is not a divisor of 4042)
...
4042 / 62 = 65.193548387097 (the remainder is 12, so 62 is not a divisor of 4042)
4042 / 63 = 64.15873015873 (the remainder is 10, so 63 is not a divisor of 4042)