What are the divisors of 4574?

1, 2, 2287, 4574

There is a total of 4 positive divisors.
The sum of these divisors is 6864.
The arithmetic mean is 1716.

2 even divisors

2, 4574

2 odd divisors

1, 2287

How to compute the divisors of 4574?

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 4574 by each of the numbers from 1 to 4574 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)

4574 / 1 = 4574 (the remainder is 0, so 1 is a divisor of 4574)
4574 / 2 = 2287 (the remainder is 0, so 2 is a divisor of 4574)
4574 / 3 = 1524.6666666667 (the remainder is 2, so 3 is not a divisor of 4574)
...
4574 / 4573 = 1.0002186748305 (the remainder is 1, so 4573 is not a divisor of 4574)
4574 / 4574 = 1 (the remainder is 0, so 4574 is a divisor of 4574)

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 4574 (i.e. 67.631353675644). 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 $\frac{N}{d} = D$ )

4574 / 1 = 4574 (the remainder is 0, so 1 and 4574 are divisors of 4574)
4574 / 2 = 2287 (the remainder is 0, so 2 and 2287 are divisors of 4574)
4574 / 3 = 1524.6666666667 (the remainder is 2, so 3 is not a divisor of 4574)
...
4574 / 66 = 69.30303030303 (the remainder is 20, so 66 is not a divisor of 4574)
4574 / 67 = 68.268656716418 (the remainder is 18, so 67 is not a divisor of 4574)