What are the divisors of 4050?

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 81, 90, 135, 150, 162, 225, 270, 405, 450, 675, 810, 1350, 2025, 4050

There is a total of 30 positive divisors.
The sum of these divisors is 11253.
The arithmetic mean is 375.1.

15 even divisors

2, 6, 10, 18, 30, 50, 54, 90, 150, 162, 270, 450, 810, 1350, 4050

15 odd divisors

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025

How to compute the divisors of 4050?

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 4050 by each of the numbers from 1 to 4050 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)

4050 / 1 = 4050 (the remainder is 0, so 1 is a divisor of 4050)
4050 / 2 = 2025 (the remainder is 0, so 2 is a divisor of 4050)
4050 / 3 = 1350 (the remainder is 0, so 3 is a divisor of 4050)
...
4050 / 4049 = 1.0002469745616 (the remainder is 1, so 4049 is not a divisor of 4050)
4050 / 4050 = 1 (the remainder is 0, so 4050 is a divisor of 4050)

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 4050 (i.e. 63.639610306789). 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 $\frac{N}{d} = D$ )

4050 / 1 = 4050 (the remainder is 0, so 1 and 4050 are divisors of 4050)
4050 / 2 = 2025 (the remainder is 0, so 2 and 2025 are divisors of 4050)
4050 / 3 = 1350 (the remainder is 0, so 3 and 1350 are divisors of 4050)
...
4050 / 62 = 65.322580645161 (the remainder is 20, so 62 is not a divisor of 4050)
4050 / 63 = 64.285714285714 (the remainder is 18, so 63 is not a divisor of 4050)