What are the divisors of 4985?

1, 5, 997, 4985

There is a total of 4 positive divisors.
The sum of these divisors is 5988.
The arithmetic mean is 1497.

4 odd divisors

1, 5, 997, 4985

How to compute the divisors of 4985?

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 4985 by each of the numbers from 1 to 4985 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)

4985 / 1 = 4985 (the remainder is 0, so 1 is a divisor of 4985)
4985 / 2 = 2492.5 (the remainder is 1, so 2 is not a divisor of 4985)
4985 / 3 = 1661.6666666667 (the remainder is 2, so 3 is not a divisor of 4985)
...
4985 / 4984 = 1.0002006420546 (the remainder is 1, so 4984 is not a divisor of 4985)
4985 / 4985 = 1 (the remainder is 0, so 4985 is a divisor of 4985)

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 4985 (i.e. 70.604532432415). 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 $\frac{N}{d} = D$ )

4985 / 1 = 4985 (the remainder is 0, so 1 and 4985 are divisors of 4985)
4985 / 2 = 2492.5 (the remainder is 1, so 2 is not a divisor of 4985)
4985 / 3 = 1661.6666666667 (the remainder is 2, so 3 is not a divisor of 4985)
...
4985 / 69 = 72.246376811594 (the remainder is 17, so 69 is not a divisor of 4985)
4985 / 70 = 71.214285714286 (the remainder is 15, so 70 is not a divisor of 4985)