What are the divisors of 4410?

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 49, 63, 70, 90, 98, 105, 126, 147, 210, 245, 294, 315, 441, 490, 630, 735, 882, 1470, 2205, 4410

There is a total of 36 positive divisors.
The sum of these divisors is 13338.
The arithmetic mean is 370.5.

18 even divisors

2, 6, 10, 14, 18, 30, 42, 70, 90, 98, 126, 210, 294, 490, 630, 882, 1470, 4410

18 odd divisors

1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205

How to compute the divisors of 4410?

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 4410 by each of the numbers from 1 to 4410 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)

4410 / 1 = 4410 (the remainder is 0, so 1 is a divisor of 4410)
4410 / 2 = 2205 (the remainder is 0, so 2 is a divisor of 4410)
4410 / 3 = 1470 (the remainder is 0, so 3 is a divisor of 4410)
...
4410 / 4409 = 1.0002268088002 (the remainder is 1, so 4409 is not a divisor of 4410)
4410 / 4410 = 1 (the remainder is 0, so 4410 is a divisor of 4410)

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 4410 (i.e. 66.407830863536). 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 $\frac{N}{d} = D$ )

4410 / 1 = 4410 (the remainder is 0, so 1 and 4410 are divisors of 4410)
4410 / 2 = 2205 (the remainder is 0, so 2 and 2205 are divisors of 4410)
4410 / 3 = 1470 (the remainder is 0, so 3 and 1470 are divisors of 4410)
...
4410 / 65 = 67.846153846154 (the remainder is 55, so 65 is not a divisor of 4410)
4410 / 66 = 66.818181818182 (the remainder is 54, so 66 is not a divisor of 4410)