What are the divisors of 4741?

1, 11, 431, 4741

There is a total of 4 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 1296.

4 odd divisors

1, 11, 431, 4741

How to compute the divisors of 4741?

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 4741 by each of the numbers from 1 to 4741 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)

4741 / 1 = 4741 (the remainder is 0, so 1 is a divisor of 4741)
4741 / 2 = 2370.5 (the remainder is 1, so 2 is not a divisor of 4741)
4741 / 3 = 1580.3333333333 (the remainder is 1, so 3 is not a divisor of 4741)
...
4741 / 4740 = 1.0002109704641 (the remainder is 1, so 4740 is not a divisor of 4741)
4741 / 4741 = 1 (the remainder is 0, so 4741 is a divisor of 4741)

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 4741 (i.e. 68.854919940408). 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 $\frac{N}{d} = D$ )

4741 / 1 = 4741 (the remainder is 0, so 1 and 4741 are divisors of 4741)
4741 / 2 = 2370.5 (the remainder is 1, so 2 is not a divisor of 4741)
4741 / 3 = 1580.3333333333 (the remainder is 1, so 3 is not a divisor of 4741)
...
4741 / 67 = 70.761194029851 (the remainder is 51, so 67 is not a divisor of 4741)
4741 / 68 = 69.720588235294 (the remainder is 49, so 68 is not a divisor of 4741)