What are the divisors of 4681?

1, 31, 151, 4681

There is a total of 4 positive divisors.
The sum of these divisors is 4864.
The arithmetic mean is 1216.

4 odd divisors

1, 31, 151, 4681

How to compute the divisors of 4681?

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 4681 by each of the numbers from 1 to 4681 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)

4681 / 1 = 4681 (the remainder is 0, so 1 is a divisor of 4681)
4681 / 2 = 2340.5 (the remainder is 1, so 2 is not a divisor of 4681)
4681 / 3 = 1560.3333333333 (the remainder is 1, so 3 is not a divisor of 4681)
...
4681 / 4680 = 1.0002136752137 (the remainder is 1, so 4680 is not a divisor of 4681)
4681 / 4681 = 1 (the remainder is 0, so 4681 is a divisor of 4681)

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 4681 (i.e. 68.417833932389). 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 $\frac{N}{d} = D$ )

4681 / 1 = 4681 (the remainder is 0, so 1 and 4681 are divisors of 4681)
4681 / 2 = 2340.5 (the remainder is 1, so 2 is not a divisor of 4681)
4681 / 3 = 1560.3333333333 (the remainder is 1, so 3 is not a divisor of 4681)
...
4681 / 67 = 69.865671641791 (the remainder is 58, so 67 is not a divisor of 4681)
4681 / 68 = 68.838235294118 (the remainder is 57, so 68 is not a divisor of 4681)