What are the divisors of 4936?

1, 2, 4, 8, 617, 1234, 2468, 4936

There is a total of 8 positive divisors.
The sum of these divisors is 9270.
The arithmetic mean is 1158.75.

6 even divisors

2, 4, 8, 1234, 2468, 4936

2 odd divisors

1, 617

How to compute the divisors of 4936?

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 4936 by each of the numbers from 1 to 4936 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)

4936 / 1 = 4936 (the remainder is 0, so 1 is a divisor of 4936)
4936 / 2 = 2468 (the remainder is 0, so 2 is a divisor of 4936)
4936 / 3 = 1645.3333333333 (the remainder is 1, so 3 is not a divisor of 4936)
...
4936 / 4935 = 1.0002026342452 (the remainder is 1, so 4935 is not a divisor of 4936)
4936 / 4936 = 1 (the remainder is 0, so 4936 is a divisor of 4936)

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 4936 (i.e. 70.256672281001). 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 $\frac{N}{d} = D$ )

4936 / 1 = 4936 (the remainder is 0, so 1 and 4936 are divisors of 4936)
4936 / 2 = 2468 (the remainder is 0, so 2 and 2468 are divisors of 4936)
4936 / 3 = 1645.3333333333 (the remainder is 1, so 3 is not a divisor of 4936)
...
4936 / 69 = 71.536231884058 (the remainder is 37, so 69 is not a divisor of 4936)
4936 / 70 = 70.514285714286 (the remainder is 36, so 70 is not a divisor of 4936)