What are the divisors of 4034?

1, 2, 2017, 4034

There is a total of 4 positive divisors.
The sum of these divisors is 6054.
The arithmetic mean is 1513.5.

2 even divisors

2, 4034

2 odd divisors

1, 2017

How to compute the divisors of 4034?

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 4034 by each of the numbers from 1 to 4034 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)

4034 / 1 = 4034 (the remainder is 0, so 1 is a divisor of 4034)
4034 / 2 = 2017 (the remainder is 0, so 2 is a divisor of 4034)
4034 / 3 = 1344.6666666667 (the remainder is 2, so 3 is not a divisor of 4034)
...
4034 / 4033 = 1.0002479543764 (the remainder is 1, so 4033 is not a divisor of 4034)
4034 / 4034 = 1 (the remainder is 0, so 4034 is a divisor of 4034)

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 4034 (i.e. 63.513778032802). 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 $\frac{N}{d} = D$ )

4034 / 1 = 4034 (the remainder is 0, so 1 and 4034 are divisors of 4034)
4034 / 2 = 2017 (the remainder is 0, so 2 and 2017 are divisors of 4034)
4034 / 3 = 1344.6666666667 (the remainder is 2, so 3 is not a divisor of 4034)
...
4034 / 62 = 65.064516129032 (the remainder is 4, so 62 is not a divisor of 4034)
4034 / 63 = 64.031746031746 (the remainder is 2, so 63 is not a divisor of 4034)