What are the divisors of 4744?

1, 2, 4, 8, 593, 1186, 2372, 4744

There is a total of 8 positive divisors.
The sum of these divisors is 8910.
The arithmetic mean is 1113.75.

6 even divisors

2, 4, 8, 1186, 2372, 4744

2 odd divisors

1, 593

How to compute the divisors of 4744?

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 4744 by each of the numbers from 1 to 4744 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)

4744 / 1 = 4744 (the remainder is 0, so 1 is a divisor of 4744)
4744 / 2 = 2372 (the remainder is 0, so 2 is a divisor of 4744)
4744 / 3 = 1581.3333333333 (the remainder is 1, so 3 is not a divisor of 4744)
...
4744 / 4743 = 1.000210837023 (the remainder is 1, so 4743 is not a divisor of 4744)
4744 / 4744 = 1 (the remainder is 0, so 4744 is a divisor of 4744)

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 4744 (i.e. 68.87670143089). 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 $\frac{N}{d} = D$ )

4744 / 1 = 4744 (the remainder is 0, so 1 and 4744 are divisors of 4744)
4744 / 2 = 2372 (the remainder is 0, so 2 and 2372 are divisors of 4744)
4744 / 3 = 1581.3333333333 (the remainder is 1, so 3 is not a divisor of 4744)
...
4744 / 67 = 70.805970149254 (the remainder is 54, so 67 is not a divisor of 4744)
4744 / 68 = 69.764705882353 (the remainder is 52, so 68 is not a divisor of 4744)