What are the divisors of 4460?

1, 2, 4, 5, 10, 20, 223, 446, 892, 1115, 2230, 4460

There is a total of 12 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 784.

8 even divisors

2, 4, 10, 20, 446, 892, 2230, 4460

4 odd divisors

1, 5, 223, 1115

How to compute the divisors of 4460?

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 4460 by each of the numbers from 1 to 4460 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)

4460 / 1 = 4460 (the remainder is 0, so 1 is a divisor of 4460)
4460 / 2 = 2230 (the remainder is 0, so 2 is a divisor of 4460)
4460 / 3 = 1486.6666666667 (the remainder is 2, so 3 is not a divisor of 4460)
...
4460 / 4459 = 1.0002242655304 (the remainder is 1, so 4459 is not a divisor of 4460)
4460 / 4460 = 1 (the remainder is 0, so 4460 is a divisor of 4460)

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 4460 (i.e. 66.783231428256). 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 $\frac{N}{d} = D$ )

4460 / 1 = 4460 (the remainder is 0, so 1 and 4460 are divisors of 4460)
4460 / 2 = 2230 (the remainder is 0, so 2 and 2230 are divisors of 4460)
4460 / 3 = 1486.6666666667 (the remainder is 2, so 3 is not a divisor of 4460)
...
4460 / 65 = 68.615384615385 (the remainder is 40, so 65 is not a divisor of 4460)
4460 / 66 = 67.575757575758 (the remainder is 38, so 66 is not a divisor of 4460)