What are the divisors of 4553?

1, 29, 157, 4553

There is a total of 4 positive divisors.
The sum of these divisors is 4740.
The arithmetic mean is 1185.

4 odd divisors

1, 29, 157, 4553

How to compute the divisors of 4553?

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 4553 by each of the numbers from 1 to 4553 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)

4553 / 1 = 4553 (the remainder is 0, so 1 is a divisor of 4553)
4553 / 2 = 2276.5 (the remainder is 1, so 2 is not a divisor of 4553)
4553 / 3 = 1517.6666666667 (the remainder is 2, so 3 is not a divisor of 4553)
...
4553 / 4552 = 1.0002196836555 (the remainder is 1, so 4552 is not a divisor of 4553)
4553 / 4553 = 1 (the remainder is 0, so 4553 is a divisor of 4553)

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 4553 (i.e. 67.475921631349). 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 $\frac{N}{d} = D$ )

4553 / 1 = 4553 (the remainder is 0, so 1 and 4553 are divisors of 4553)
4553 / 2 = 2276.5 (the remainder is 1, so 2 is not a divisor of 4553)
4553 / 3 = 1517.6666666667 (the remainder is 2, so 3 is not a divisor of 4553)
...
4553 / 66 = 68.984848484848 (the remainder is 65, so 66 is not a divisor of 4553)
4553 / 67 = 67.955223880597 (the remainder is 64, so 67 is not a divisor of 4553)