What are the divisors of 4645?

1, 5, 929, 4645

There is a total of 4 positive divisors.
The sum of these divisors is 5580.
The arithmetic mean is 1395.

4 odd divisors

1, 5, 929, 4645

How to compute the divisors of 4645?

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 4645 by each of the numbers from 1 to 4645 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)

4645 / 1 = 4645 (the remainder is 0, so 1 is a divisor of 4645)
4645 / 2 = 2322.5 (the remainder is 1, so 2 is not a divisor of 4645)
4645 / 3 = 1548.3333333333 (the remainder is 1, so 3 is not a divisor of 4645)
...
4645 / 4644 = 1.0002153316107 (the remainder is 1, so 4644 is not a divisor of 4645)
4645 / 4645 = 1 (the remainder is 0, so 4645 is a divisor of 4645)

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 4645 (i.e. 68.154236845555). 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 $\frac{N}{d} = D$ )

4645 / 1 = 4645 (the remainder is 0, so 1 and 4645 are divisors of 4645)
4645 / 2 = 2322.5 (the remainder is 1, so 2 is not a divisor of 4645)
4645 / 3 = 1548.3333333333 (the remainder is 1, so 3 is not a divisor of 4645)
...
4645 / 67 = 69.328358208955 (the remainder is 22, so 67 is not a divisor of 4645)
4645 / 68 = 68.308823529412 (the remainder is 21, so 68 is not a divisor of 4645)