What are the divisors of 4637?

1, 4637

There is a total of 2 positive divisors.
The sum of these divisors is 4638.
The arithmetic mean is 2319.

2 odd divisors

1, 4637

How to compute the divisors of 4637?

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 4637 by each of the numbers from 1 to 4637 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)

4637 / 1 = 4637 (the remainder is 0, so 1 is a divisor of 4637)
4637 / 2 = 2318.5 (the remainder is 1, so 2 is not a divisor of 4637)
4637 / 3 = 1545.6666666667 (the remainder is 2, so 3 is not a divisor of 4637)
...
4637 / 4636 = 1.0002157031924 (the remainder is 1, so 4636 is not a divisor of 4637)
4637 / 4637 = 1 (the remainder is 0, so 4637 is a divisor of 4637)

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 4637 (i.e. 68.095521144933). 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 $\frac{N}{d} = D$ )

4637 / 1 = 4637 (the remainder is 0, so 1 and 4637 are divisors of 4637)
4637 / 2 = 2318.5 (the remainder is 1, so 2 is not a divisor of 4637)
4637 / 3 = 1545.6666666667 (the remainder is 2, so 3 is not a divisor of 4637)
...
4637 / 67 = 69.208955223881 (the remainder is 14, so 67 is not a divisor of 4637)
4637 / 68 = 68.191176470588 (the remainder is 13, so 68 is not a divisor of 4637)