What are the divisors of 4258?

1, 2, 2129, 4258

There is a total of 4 positive divisors.
The sum of these divisors is 6390.
The arithmetic mean is 1597.5.

2 even divisors

2, 4258

2 odd divisors

1, 2129

How to compute the divisors of 4258?

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 4258 by each of the numbers from 1 to 4258 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)

4258 / 1 = 4258 (the remainder is 0, so 1 is a divisor of 4258)
4258 / 2 = 2129 (the remainder is 0, so 2 is a divisor of 4258)
4258 / 3 = 1419.3333333333 (the remainder is 1, so 3 is not a divisor of 4258)
...
4258 / 4257 = 1.0002349072117 (the remainder is 1, so 4257 is not a divisor of 4258)
4258 / 4258 = 1 (the remainder is 0, so 4258 is a divisor of 4258)

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 4258 (i.e. 65.253352404302). 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 $\frac{N}{d} = D$ )

4258 / 1 = 4258 (the remainder is 0, so 1 and 4258 are divisors of 4258)
4258 / 2 = 2129 (the remainder is 0, so 2 and 2129 are divisors of 4258)
4258 / 3 = 1419.3333333333 (the remainder is 1, so 3 is not a divisor of 4258)
...
4258 / 64 = 66.53125 (the remainder is 34, so 64 is not a divisor of 4258)
4258 / 65 = 65.507692307692 (the remainder is 33, so 65 is not a divisor of 4258)