What are the divisors of 4880?

1, 2, 4, 5, 8, 10, 16, 20, 40, 61, 80, 122, 244, 305, 488, 610, 976, 1220, 2440, 4880

There is a total of 20 positive divisors.
The sum of these divisors is 11532.
The arithmetic mean is 576.6.

16 even divisors

2, 4, 8, 10, 16, 20, 40, 80, 122, 244, 488, 610, 976, 1220, 2440, 4880

4 odd divisors

1, 5, 61, 305

How to compute the divisors of 4880?

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 4880 by each of the numbers from 1 to 4880 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)

4880 / 1 = 4880 (the remainder is 0, so 1 is a divisor of 4880)
4880 / 2 = 2440 (the remainder is 0, so 2 is a divisor of 4880)
4880 / 3 = 1626.6666666667 (the remainder is 2, so 3 is not a divisor of 4880)
...
4880 / 4879 = 1.0002049600328 (the remainder is 1, so 4879 is not a divisor of 4880)
4880 / 4880 = 1 (the remainder is 0, so 4880 is a divisor of 4880)

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 4880 (i.e. 69.856996786292). 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 $\frac{N}{d} = D$ )

4880 / 1 = 4880 (the remainder is 0, so 1 and 4880 are divisors of 4880)
4880 / 2 = 2440 (the remainder is 0, so 2 and 2440 are divisors of 4880)
4880 / 3 = 1626.6666666667 (the remainder is 2, so 3 is not a divisor of 4880)
...
4880 / 68 = 71.764705882353 (the remainder is 52, so 68 is not a divisor of 4880)
4880 / 69 = 70.724637681159 (the remainder is 50, so 69 is not a divisor of 4880)