What are the divisors of 4613?

1, 7, 659, 4613

There is a total of 4 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 1320.

4 odd divisors

1, 7, 659, 4613

How to compute the divisors of 4613?

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 4613 by each of the numbers from 1 to 4613 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)

4613 / 1 = 4613 (the remainder is 0, so 1 is a divisor of 4613)
4613 / 2 = 2306.5 (the remainder is 1, so 2 is not a divisor of 4613)
4613 / 3 = 1537.6666666667 (the remainder is 2, so 3 is not a divisor of 4613)
...
4613 / 4612 = 1.0002168256722 (the remainder is 1, so 4612 is not a divisor of 4613)
4613 / 4613 = 1 (the remainder is 0, so 4613 is a divisor of 4613)

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 4613 (i.e. 67.919069487148). 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 $\frac{N}{d} = D$ )

4613 / 1 = 4613 (the remainder is 0, so 1 and 4613 are divisors of 4613)
4613 / 2 = 2306.5 (the remainder is 1, so 2 is not a divisor of 4613)
4613 / 3 = 1537.6666666667 (the remainder is 2, so 3 is not a divisor of 4613)
...
4613 / 66 = 69.893939393939 (the remainder is 59, so 66 is not a divisor of 4613)
4613 / 67 = 68.850746268657 (the remainder is 57, so 67 is not a divisor of 4613)