What are the divisors of 4457?

1, 4457

There is a total of 2 positive divisors.
The sum of these divisors is 4458.
The arithmetic mean is 2229.

2 odd divisors

1, 4457

How to compute the divisors of 4457?

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 4457 by each of the numbers from 1 to 4457 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)

4457 / 1 = 4457 (the remainder is 0, so 1 is a divisor of 4457)
4457 / 2 = 2228.5 (the remainder is 1, so 2 is not a divisor of 4457)
4457 / 3 = 1485.6666666667 (the remainder is 2, so 3 is not a divisor of 4457)
...
4457 / 4456 = 1.0002244165171 (the remainder is 1, so 4456 is not a divisor of 4457)
4457 / 4457 = 1 (the remainder is 0, so 4457 is a divisor of 4457)

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 4457 (i.e. 66.760766921898). 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 $\frac{N}{d} = D$ )

4457 / 1 = 4457 (the remainder is 0, so 1 and 4457 are divisors of 4457)
4457 / 2 = 2228.5 (the remainder is 1, so 2 is not a divisor of 4457)
4457 / 3 = 1485.6666666667 (the remainder is 2, so 3 is not a divisor of 4457)
...
4457 / 65 = 68.569230769231 (the remainder is 37, so 65 is not a divisor of 4457)
4457 / 66 = 67.530303030303 (the remainder is 35, so 66 is not a divisor of 4457)