What are the divisors of 4490?

1, 2, 5, 10, 449, 898, 2245, 4490

There is a total of 8 positive divisors.
The sum of these divisors is 8100.
The arithmetic mean is 1012.5.

4 even divisors

2, 10, 898, 4490

4 odd divisors

1, 5, 449, 2245

How to compute the divisors of 4490?

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 4490 by each of the numbers from 1 to 4490 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)

4490 / 1 = 4490 (the remainder is 0, so 1 is a divisor of 4490)
4490 / 2 = 2245 (the remainder is 0, so 2 is a divisor of 4490)
4490 / 3 = 1496.6666666667 (the remainder is 2, so 3 is not a divisor of 4490)
...
4490 / 4489 = 1.0002227667632 (the remainder is 1, so 4489 is not a divisor of 4490)
4490 / 4490 = 1 (the remainder is 0, so 4490 is a divisor of 4490)

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 4490 (i.e. 67.007462271004). 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 $\frac{N}{d} = D$ )

4490 / 1 = 4490 (the remainder is 0, so 1 and 4490 are divisors of 4490)
4490 / 2 = 2245 (the remainder is 0, so 2 and 2245 are divisors of 4490)
4490 / 3 = 1496.6666666667 (the remainder is 2, so 3 is not a divisor of 4490)
...
4490 / 66 = 68.030303030303 (the remainder is 2, so 66 is not a divisor of 4490)
4490 / 67 = 67.014925373134 (the remainder is 1, so 67 is not a divisor of 4490)