What are the divisors of 4024?

1, 2, 4, 8, 503, 1006, 2012, 4024

There is a total of 8 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 945.

6 even divisors

2, 4, 8, 1006, 2012, 4024

2 odd divisors

1, 503

How to compute the divisors of 4024?

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 4024 by each of the numbers from 1 to 4024 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)

4024 / 1 = 4024 (the remainder is 0, so 1 is a divisor of 4024)
4024 / 2 = 2012 (the remainder is 0, so 2 is a divisor of 4024)
4024 / 3 = 1341.3333333333 (the remainder is 1, so 3 is not a divisor of 4024)
...
4024 / 4023 = 1.0002485707184 (the remainder is 1, so 4023 is not a divisor of 4024)
4024 / 4024 = 1 (the remainder is 0, so 4024 is a divisor of 4024)

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 4024 (i.e. 63.435006108615). 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 $\frac{N}{d} = D$ )

4024 / 1 = 4024 (the remainder is 0, so 1 and 4024 are divisors of 4024)
4024 / 2 = 2012 (the remainder is 0, so 2 and 2012 are divisors of 4024)
4024 / 3 = 1341.3333333333 (the remainder is 1, so 3 is not a divisor of 4024)
...
4024 / 62 = 64.903225806452 (the remainder is 56, so 62 is not a divisor of 4024)
4024 / 63 = 63.873015873016 (the remainder is 55, so 63 is not a divisor of 4024)