What are the divisors of 4420?

1, 2, 4, 5, 10, 13, 17, 20, 26, 34, 52, 65, 68, 85, 130, 170, 221, 260, 340, 442, 884, 1105, 2210, 4420

There is a total of 24 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 441.

16 even divisors

2, 4, 10, 20, 26, 34, 52, 68, 130, 170, 260, 340, 442, 884, 2210, 4420

8 odd divisors

1, 5, 13, 17, 65, 85, 221, 1105

How to compute the divisors of 4420?

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 4420 by each of the numbers from 1 to 4420 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)

4420 / 1 = 4420 (the remainder is 0, so 1 is a divisor of 4420)
4420 / 2 = 2210 (the remainder is 0, so 2 is a divisor of 4420)
4420 / 3 = 1473.3333333333 (the remainder is 1, so 3 is not a divisor of 4420)
...
4420 / 4419 = 1.000226295542 (the remainder is 1, so 4419 is not a divisor of 4420)
4420 / 4420 = 1 (the remainder is 0, so 4420 is a divisor of 4420)

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 4420 (i.e. 66.483080554379). 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 $\frac{N}{d} = D$ )

4420 / 1 = 4420 (the remainder is 0, so 1 and 4420 are divisors of 4420)
4420 / 2 = 2210 (the remainder is 0, so 2 and 2210 are divisors of 4420)
4420 / 3 = 1473.3333333333 (the remainder is 1, so 3 is not a divisor of 4420)
...
4420 / 65 = 68 (the remainder is 0, so 65 and 68 are divisors of 4420)
4420 / 66 = 66.969696969697 (the remainder is 64, so 66 is not a divisor of 4420)