What are the divisors of 4546?

1, 2, 2273, 4546

There is a total of 4 positive divisors.
The sum of these divisors is 6822.
The arithmetic mean is 1705.5.

2 even divisors

2, 4546

2 odd divisors

1, 2273

How to compute the divisors of 4546?

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 4546 by each of the numbers from 1 to 4546 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)

4546 / 1 = 4546 (the remainder is 0, so 1 is a divisor of 4546)
4546 / 2 = 2273 (the remainder is 0, so 2 is a divisor of 4546)
4546 / 3 = 1515.3333333333 (the remainder is 1, so 3 is not a divisor of 4546)
...
4546 / 4545 = 1.0002200220022 (the remainder is 1, so 4545 is not a divisor of 4546)
4546 / 4546 = 1 (the remainder is 0, so 4546 is a divisor of 4546)

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 4546 (i.e. 67.42403132415). 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 $\frac{N}{d} = D$ )

4546 / 1 = 4546 (the remainder is 0, so 1 and 4546 are divisors of 4546)
4546 / 2 = 2273 (the remainder is 0, so 2 and 2273 are divisors of 4546)
4546 / 3 = 1515.3333333333 (the remainder is 1, so 3 is not a divisor of 4546)
...
4546 / 66 = 68.878787878788 (the remainder is 58, so 66 is not a divisor of 4546)
4546 / 67 = 67.850746268657 (the remainder is 57, so 67 is not a divisor of 4546)