What are the divisors of 4981?

1, 17, 293, 4981

There is a total of 4 positive divisors.
The sum of these divisors is 5292.
The arithmetic mean is 1323.

4 odd divisors

1, 17, 293, 4981

How to compute the divisors of 4981?

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 4981 by each of the numbers from 1 to 4981 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)

4981 / 1 = 4981 (the remainder is 0, so 1 is a divisor of 4981)
4981 / 2 = 2490.5 (the remainder is 1, so 2 is not a divisor of 4981)
4981 / 3 = 1660.3333333333 (the remainder is 1, so 3 is not a divisor of 4981)
...
4981 / 4980 = 1.0002008032129 (the remainder is 1, so 4980 is not a divisor of 4981)
4981 / 4981 = 1 (the remainder is 0, so 4981 is a divisor of 4981)

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 4981 (i.e. 70.576199954376). 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 $\frac{N}{d} = D$ )

4981 / 1 = 4981 (the remainder is 0, so 1 and 4981 are divisors of 4981)
4981 / 2 = 2490.5 (the remainder is 1, so 2 is not a divisor of 4981)
4981 / 3 = 1660.3333333333 (the remainder is 1, so 3 is not a divisor of 4981)
...
4981 / 69 = 72.188405797101 (the remainder is 13, so 69 is not a divisor of 4981)
4981 / 70 = 71.157142857143 (the remainder is 11, so 70 is not a divisor of 4981)