What are the divisors of 4895?

1, 5, 11, 55, 89, 445, 979, 4895

There is a total of 8 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 810.

8 odd divisors

1, 5, 11, 55, 89, 445, 979, 4895

How to compute the divisors of 4895?

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 4895 by each of the numbers from 1 to 4895 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)

4895 / 1 = 4895 (the remainder is 0, so 1 is a divisor of 4895)
4895 / 2 = 2447.5 (the remainder is 1, so 2 is not a divisor of 4895)
4895 / 3 = 1631.6666666667 (the remainder is 2, so 3 is not a divisor of 4895)
...
4895 / 4894 = 1.0002043318349 (the remainder is 1, so 4894 is not a divisor of 4895)
4895 / 4895 = 1 (the remainder is 0, so 4895 is a divisor of 4895)

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 4895 (i.e. 69.964276598847). 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 $\frac{N}{d} = D$ )

4895 / 1 = 4895 (the remainder is 0, so 1 and 4895 are divisors of 4895)
4895 / 2 = 2447.5 (the remainder is 1, so 2 is not a divisor of 4895)
4895 / 3 = 1631.6666666667 (the remainder is 2, so 3 is not a divisor of 4895)
...
4895 / 68 = 71.985294117647 (the remainder is 67, so 68 is not a divisor of 4895)
4895 / 69 = 70.942028985507 (the remainder is 65, so 69 is not a divisor of 4895)