What are the divisors of 4033?

1, 37, 109, 4033

There is a total of 4 positive divisors.
The sum of these divisors is 4180.
The arithmetic mean is 1045.

4 odd divisors

1, 37, 109, 4033

How to compute the divisors of 4033?

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 4033 by each of the numbers from 1 to 4033 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)

4033 / 1 = 4033 (the remainder is 0, so 1 is a divisor of 4033)
4033 / 2 = 2016.5 (the remainder is 1, so 2 is not a divisor of 4033)
4033 / 3 = 1344.3333333333 (the remainder is 1, so 3 is not a divisor of 4033)
...
4033 / 4032 = 1.000248015873 (the remainder is 1, so 4032 is not a divisor of 4033)
4033 / 4033 = 1 (the remainder is 0, so 4033 is a divisor of 4033)

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 4033 (i.e. 63.50590523723). 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 $\frac{N}{d} = D$ )

4033 / 1 = 4033 (the remainder is 0, so 1 and 4033 are divisors of 4033)
4033 / 2 = 2016.5 (the remainder is 1, so 2 is not a divisor of 4033)
4033 / 3 = 1344.3333333333 (the remainder is 1, so 3 is not a divisor of 4033)
...
4033 / 62 = 65.048387096774 (the remainder is 3, so 62 is not a divisor of 4033)
4033 / 63 = 64.015873015873 (the remainder is 1, so 63 is not a divisor of 4033)