What are the divisors of 4840?

1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 121, 220, 242, 440, 484, 605, 968, 1210, 2420, 4840

There is a total of 24 positive divisors.
The sum of these divisors is 11970.
The arithmetic mean is 498.75.

18 even divisors

2, 4, 8, 10, 20, 22, 40, 44, 88, 110, 220, 242, 440, 484, 968, 1210, 2420, 4840

6 odd divisors

1, 5, 11, 55, 121, 605

How to compute the divisors of 4840?

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 4840 by each of the numbers from 1 to 4840 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)

4840 / 1 = 4840 (the remainder is 0, so 1 is a divisor of 4840)
4840 / 2 = 2420 (the remainder is 0, so 2 is a divisor of 4840)
4840 / 3 = 1613.3333333333 (the remainder is 1, so 3 is not a divisor of 4840)
...
4840 / 4839 = 1.0002066542674 (the remainder is 1, so 4839 is not a divisor of 4840)
4840 / 4840 = 1 (the remainder is 0, so 4840 is a divisor of 4840)

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 4840 (i.e. 69.570108523704). 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 $\frac{N}{d} = D$ )

4840 / 1 = 4840 (the remainder is 0, so 1 and 4840 are divisors of 4840)
4840 / 2 = 2420 (the remainder is 0, so 2 and 2420 are divisors of 4840)
4840 / 3 = 1613.3333333333 (the remainder is 1, so 3 is not a divisor of 4840)
...
4840 / 68 = 71.176470588235 (the remainder is 12, so 68 is not a divisor of 4840)
4840 / 69 = 70.144927536232 (the remainder is 10, so 69 is not a divisor of 4840)