What are the divisors of 4348?

1, 2, 4, 1087, 2174, 4348

There is a total of 6 positive divisors.
The sum of these divisors is 7616.
The arithmetic mean is 1269.3333333333.

4 even divisors

2, 4, 2174, 4348

2 odd divisors

1, 1087

How to compute the divisors of 4348?

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 4348 by each of the numbers from 1 to 4348 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)

4348 / 1 = 4348 (the remainder is 0, so 1 is a divisor of 4348)
4348 / 2 = 2174 (the remainder is 0, so 2 is a divisor of 4348)
4348 / 3 = 1449.3333333333 (the remainder is 1, so 3 is not a divisor of 4348)
...
4348 / 4347 = 1.0002300437083 (the remainder is 1, so 4347 is not a divisor of 4348)
4348 / 4348 = 1 (the remainder is 0, so 4348 is a divisor of 4348)

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 4348 (i.e. 65.939366087338). 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 $\frac{N}{d} = D$ )

4348 / 1 = 4348 (the remainder is 0, so 1 and 4348 are divisors of 4348)
4348 / 2 = 2174 (the remainder is 0, so 2 and 2174 are divisors of 4348)
4348 / 3 = 1449.3333333333 (the remainder is 1, so 3 is not a divisor of 4348)
...
4348 / 64 = 67.9375 (the remainder is 60, so 64 is not a divisor of 4348)
4348 / 65 = 66.892307692308 (the remainder is 58, so 65 is not a divisor of 4348)