What are the divisors of 4986?

1, 2, 3, 6, 9, 18, 277, 554, 831, 1662, 2493, 4986

There is a total of 12 positive divisors.
The sum of these divisors is 10842.
The arithmetic mean is 903.5.

6 even divisors

2, 6, 18, 554, 1662, 4986

6 odd divisors

1, 3, 9, 277, 831, 2493

How to compute the divisors of 4986?

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 4986 by each of the numbers from 1 to 4986 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)

4986 / 1 = 4986 (the remainder is 0, so 1 is a divisor of 4986)
4986 / 2 = 2493 (the remainder is 0, so 2 is a divisor of 4986)
4986 / 3 = 1662 (the remainder is 0, so 3 is a divisor of 4986)
...
4986 / 4985 = 1.0002006018054 (the remainder is 1, so 4985 is not a divisor of 4986)
4986 / 4986 = 1 (the remainder is 0, so 4986 is a divisor of 4986)

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 4986 (i.e. 70.611613775639). 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 $\frac{N}{d} = D$ )

4986 / 1 = 4986 (the remainder is 0, so 1 and 4986 are divisors of 4986)
4986 / 2 = 2493 (the remainder is 0, so 2 and 2493 are divisors of 4986)
4986 / 3 = 1662 (the remainder is 0, so 3 and 1662 are divisors of 4986)
...
4986 / 69 = 72.260869565217 (the remainder is 18, so 69 is not a divisor of 4986)
4986 / 70 = 71.228571428571 (the remainder is 16, so 70 is not a divisor of 4986)