What are the divisors of 4885?

1, 5, 977, 4885

There is a total of 4 positive divisors.
The sum of these divisors is 5868.
The arithmetic mean is 1467.

4 odd divisors

1, 5, 977, 4885

How to compute the divisors of 4885?

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 4885 by each of the numbers from 1 to 4885 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)

4885 / 1 = 4885 (the remainder is 0, so 1 is a divisor of 4885)
4885 / 2 = 2442.5 (the remainder is 1, so 2 is not a divisor of 4885)
4885 / 3 = 1628.3333333333 (the remainder is 1, so 3 is not a divisor of 4885)
...
4885 / 4884 = 1.0002047502048 (the remainder is 1, so 4884 is not a divisor of 4885)
4885 / 4885 = 1 (the remainder is 0, so 4885 is a divisor of 4885)

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 4885 (i.e. 69.892775020026). 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 $\frac{N}{d} = D$ )

4885 / 1 = 4885 (the remainder is 0, so 1 and 4885 are divisors of 4885)
4885 / 2 = 2442.5 (the remainder is 1, so 2 is not a divisor of 4885)
4885 / 3 = 1628.3333333333 (the remainder is 1, so 3 is not a divisor of 4885)
...
4885 / 68 = 71.838235294118 (the remainder is 57, so 68 is not a divisor of 4885)
4885 / 69 = 70.797101449275 (the remainder is 55, so 69 is not a divisor of 4885)