What are the divisors of 4830?

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 23, 30, 35, 42, 46, 69, 70, 105, 115, 138, 161, 210, 230, 322, 345, 483, 690, 805, 966, 1610, 2415, 4830

There is a total of 32 positive divisors.
The sum of these divisors is 13824.
The arithmetic mean is 432.

16 even divisors

2, 6, 10, 14, 30, 42, 46, 70, 138, 210, 230, 322, 690, 966, 1610, 4830

16 odd divisors

1, 3, 5, 7, 15, 21, 23, 35, 69, 105, 115, 161, 345, 483, 805, 2415

How to compute the divisors of 4830?

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 4830 by each of the numbers from 1 to 4830 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)

4830 / 1 = 4830 (the remainder is 0, so 1 is a divisor of 4830)
4830 / 2 = 2415 (the remainder is 0, so 2 is a divisor of 4830)
4830 / 3 = 1610 (the remainder is 0, so 3 is a divisor of 4830)
...
4830 / 4829 = 1.0002070822116 (the remainder is 1, so 4829 is not a divisor of 4830)
4830 / 4830 = 1 (the remainder is 0, so 4830 is a divisor of 4830)

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 4830 (i.e. 69.498201415576). 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 $\frac{N}{d} = D$ )

4830 / 1 = 4830 (the remainder is 0, so 1 and 4830 are divisors of 4830)
4830 / 2 = 2415 (the remainder is 0, so 2 and 2415 are divisors of 4830)
4830 / 3 = 1610 (the remainder is 0, so 3 and 1610 are divisors of 4830)
...
4830 / 68 = 71.029411764706 (the remainder is 2, so 68 is not a divisor of 4830)
4830 / 69 = 70 (the remainder is 0, so 69 and 70 are divisors of 4830)