What are the divisors of 4820?

1, 2, 4, 5, 10, 20, 241, 482, 964, 1205, 2410, 4820

There is a total of 12 positive divisors.
The sum of these divisors is 10164.
The arithmetic mean is 847.

8 even divisors

2, 4, 10, 20, 482, 964, 2410, 4820

4 odd divisors

1, 5, 241, 1205

How to compute the divisors of 4820?

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 4820 by each of the numbers from 1 to 4820 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)

4820 / 1 = 4820 (the remainder is 0, so 1 is a divisor of 4820)
4820 / 2 = 2410 (the remainder is 0, so 2 is a divisor of 4820)
4820 / 3 = 1606.6666666667 (the remainder is 2, so 3 is not a divisor of 4820)
...
4820 / 4819 = 1.0002075119319 (the remainder is 1, so 4819 is not a divisor of 4820)
4820 / 4820 = 1 (the remainder is 0, so 4820 is a divisor of 4820)

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 4820 (i.e. 69.426219830839). 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 $\frac{N}{d} = D$ )

4820 / 1 = 4820 (the remainder is 0, so 1 and 4820 are divisors of 4820)
4820 / 2 = 2410 (the remainder is 0, so 2 and 2410 are divisors of 4820)
4820 / 3 = 1606.6666666667 (the remainder is 2, so 3 is not a divisor of 4820)
...
4820 / 68 = 70.882352941176 (the remainder is 60, so 68 is not a divisor of 4820)
4820 / 69 = 69.855072463768 (the remainder is 59, so 69 is not a divisor of 4820)