What are the divisors of 4943?

1, 4943

There is a total of 2 positive divisors.
The sum of these divisors is 4944.
The arithmetic mean is 2472.

2 odd divisors

1, 4943

How to compute the divisors of 4943?

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 4943 by each of the numbers from 1 to 4943 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)

4943 / 1 = 4943 (the remainder is 0, so 1 is a divisor of 4943)
4943 / 2 = 2471.5 (the remainder is 1, so 2 is not a divisor of 4943)
4943 / 3 = 1647.6666666667 (the remainder is 2, so 3 is not a divisor of 4943)
...
4943 / 4942 = 1.0002023472278 (the remainder is 1, so 4942 is not a divisor of 4943)
4943 / 4943 = 1 (the remainder is 0, so 4943 is a divisor of 4943)

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 4943 (i.e. 70.306471963824). 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 $\frac{N}{d} = D$ )

4943 / 1 = 4943 (the remainder is 0, so 1 and 4943 are divisors of 4943)
4943 / 2 = 2471.5 (the remainder is 1, so 2 is not a divisor of 4943)
4943 / 3 = 1647.6666666667 (the remainder is 2, so 3 is not a divisor of 4943)
...
4943 / 69 = 71.63768115942 (the remainder is 44, so 69 is not a divisor of 4943)
4943 / 70 = 70.614285714286 (the remainder is 43, so 70 is not a divisor of 4943)