What are the divisors of 4290?

1, 2, 3, 5, 6, 10, 11, 13, 15, 22, 26, 30, 33, 39, 55, 65, 66, 78, 110, 130, 143, 165, 195, 286, 330, 390, 429, 715, 858, 1430, 2145, 4290

There is a total of 32 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 378.

16 even divisors

2, 6, 10, 22, 26, 30, 66, 78, 110, 130, 286, 330, 390, 858, 1430, 4290

16 odd divisors

1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145

How to compute the divisors of 4290?

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 4290 by each of the numbers from 1 to 4290 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)

4290 / 1 = 4290 (the remainder is 0, so 1 is a divisor of 4290)
4290 / 2 = 2145 (the remainder is 0, so 2 is a divisor of 4290)
4290 / 3 = 1430 (the remainder is 0, so 3 is a divisor of 4290)
...
4290 / 4289 = 1.0002331545815 (the remainder is 1, so 4289 is not a divisor of 4290)
4290 / 4290 = 1 (the remainder is 0, so 4290 is a divisor of 4290)

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 4290 (i.e. 65.498091575251). 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 $\frac{N}{d} = D$ )

4290 / 1 = 4290 (the remainder is 0, so 1 and 4290 are divisors of 4290)
4290 / 2 = 2145 (the remainder is 0, so 2 and 2145 are divisors of 4290)
4290 / 3 = 1430 (the remainder is 0, so 3 and 1430 are divisors of 4290)
...
4290 / 64 = 67.03125 (the remainder is 2, so 64 is not a divisor of 4290)
4290 / 65 = 66 (the remainder is 0, so 65 and 66 are divisors of 4290)