What are the divisors of 4933?

1, 4933

There is a total of 2 positive divisors.
The sum of these divisors is 4934.
The arithmetic mean is 2467.

2 odd divisors

1, 4933

How to compute the divisors of 4933?

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 4933 by each of the numbers from 1 to 4933 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)

4933 / 1 = 4933 (the remainder is 0, so 1 is a divisor of 4933)
4933 / 2 = 2466.5 (the remainder is 1, so 2 is not a divisor of 4933)
4933 / 3 = 1644.3333333333 (the remainder is 1, so 3 is not a divisor of 4933)
...
4933 / 4932 = 1.000202757502 (the remainder is 1, so 4932 is not a divisor of 4933)
4933 / 4933 = 1 (the remainder is 0, so 4933 is a divisor of 4933)

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 4933 (i.e. 70.235318750611). 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 $\frac{N}{d} = D$ )

4933 / 1 = 4933 (the remainder is 0, so 1 and 4933 are divisors of 4933)
4933 / 2 = 2466.5 (the remainder is 1, so 2 is not a divisor of 4933)
4933 / 3 = 1644.3333333333 (the remainder is 1, so 3 is not a divisor of 4933)
...
4933 / 69 = 71.492753623188 (the remainder is 34, so 69 is not a divisor of 4933)
4933 / 70 = 70.471428571429 (the remainder is 33, so 70 is not a divisor of 4933)