What are the divisors of 4959?

1, 3, 9, 19, 29, 57, 87, 171, 261, 551, 1653, 4959

There is a total of 12 positive divisors.
The sum of these divisors is 7800.
The arithmetic mean is 650.

12 odd divisors

1, 3, 9, 19, 29, 57, 87, 171, 261, 551, 1653, 4959

How to compute the divisors of 4959?

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 4959 by each of the numbers from 1 to 4959 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)

4959 / 1 = 4959 (the remainder is 0, so 1 is a divisor of 4959)
4959 / 2 = 2479.5 (the remainder is 1, so 2 is not a divisor of 4959)
4959 / 3 = 1653 (the remainder is 0, so 3 is a divisor of 4959)
...
4959 / 4958 = 1.0002016942315 (the remainder is 1, so 4958 is not a divisor of 4959)
4959 / 4959 = 1 (the remainder is 0, so 4959 is a divisor of 4959)

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 4959 (i.e. 70.420167565833). 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 $\frac{N}{d} = D$ )

4959 / 1 = 4959 (the remainder is 0, so 1 and 4959 are divisors of 4959)
4959 / 2 = 2479.5 (the remainder is 1, so 2 is not a divisor of 4959)
4959 / 3 = 1653 (the remainder is 0, so 3 and 1653 are divisors of 4959)
...
4959 / 69 = 71.869565217391 (the remainder is 60, so 69 is not a divisor of 4959)
4959 / 70 = 70.842857142857 (the remainder is 59, so 70 is not a divisor of 4959)