What are the divisors of 4886?

1, 2, 7, 14, 349, 698, 2443, 4886

There is a total of 8 positive divisors.
The sum of these divisors is 8400.
The arithmetic mean is 1050.

4 even divisors

2, 14, 698, 4886

4 odd divisors

1, 7, 349, 2443

How to compute the divisors of 4886?

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 4886 by each of the numbers from 1 to 4886 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)

4886 / 1 = 4886 (the remainder is 0, so 1 is a divisor of 4886)
4886 / 2 = 2443 (the remainder is 0, so 2 is a divisor of 4886)
4886 / 3 = 1628.6666666667 (the remainder is 2, so 3 is not a divisor of 4886)
...
4886 / 4885 = 1.0002047082907 (the remainder is 1, so 4885 is not a divisor of 4886)
4886 / 4886 = 1 (the remainder is 0, so 4886 is a divisor of 4886)

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 4886 (i.e. 69.899928469205). 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 $\frac{N}{d} = D$ )

4886 / 1 = 4886 (the remainder is 0, so 1 and 4886 are divisors of 4886)
4886 / 2 = 2443 (the remainder is 0, so 2 and 2443 are divisors of 4886)
4886 / 3 = 1628.6666666667 (the remainder is 2, so 3 is not a divisor of 4886)
...
4886 / 68 = 71.852941176471 (the remainder is 58, so 68 is not a divisor of 4886)
4886 / 69 = 70.811594202899 (the remainder is 56, so 69 is not a divisor of 4886)