What are the divisors of 4480?

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 280, 320, 448, 560, 640, 896, 1120, 2240, 4480

There is a total of 32 positive divisors.
The sum of these divisors is 12240.
The arithmetic mean is 382.5.

28 even divisors

2, 4, 8, 10, 14, 16, 20, 28, 32, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 280, 320, 448, 560, 640, 896, 1120, 2240, 4480

4 odd divisors

1, 5, 7, 35

How to compute the divisors of 4480?

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 4480 by each of the numbers from 1 to 4480 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)

4480 / 1 = 4480 (the remainder is 0, so 1 is a divisor of 4480)
4480 / 2 = 2240 (the remainder is 0, so 2 is a divisor of 4480)
4480 / 3 = 1493.3333333333 (the remainder is 1, so 3 is not a divisor of 4480)
...
4480 / 4479 = 1.0002232641215 (the remainder is 1, so 4479 is not a divisor of 4480)
4480 / 4480 = 1 (the remainder is 0, so 4480 is a divisor of 4480)

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 4480 (i.e. 66.932802122726). 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 $\frac{N}{d} = D$ )

4480 / 1 = 4480 (the remainder is 0, so 1 and 4480 are divisors of 4480)
4480 / 2 = 2240 (the remainder is 0, so 2 and 2240 are divisors of 4480)
4480 / 3 = 1493.3333333333 (the remainder is 1, so 3 is not a divisor of 4480)
...
4480 / 65 = 68.923076923077 (the remainder is 60, so 65 is not a divisor of 4480)
4480 / 66 = 67.878787878788 (the remainder is 58, so 66 is not a divisor of 4480)