What are the divisors of 4269?

1, 3, 1423, 4269

There is a total of 4 positive divisors.
The sum of these divisors is 5696.
The arithmetic mean is 1424.

4 odd divisors

1, 3, 1423, 4269

How to compute the divisors of 4269?

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 4269 by each of the numbers from 1 to 4269 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)

4269 / 1 = 4269 (the remainder is 0, so 1 is a divisor of 4269)
4269 / 2 = 2134.5 (the remainder is 1, so 2 is not a divisor of 4269)
4269 / 3 = 1423 (the remainder is 0, so 3 is a divisor of 4269)
...
4269 / 4268 = 1.0002343017807 (the remainder is 1, so 4268 is not a divisor of 4269)
4269 / 4269 = 1 (the remainder is 0, so 4269 is a divisor of 4269)

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 4269 (i.e. 65.337584895679). 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 $\frac{N}{d} = D$ )

4269 / 1 = 4269 (the remainder is 0, so 1 and 4269 are divisors of 4269)
4269 / 2 = 2134.5 (the remainder is 1, so 2 is not a divisor of 4269)
4269 / 3 = 1423 (the remainder is 0, so 3 and 1423 are divisors of 4269)
...
4269 / 64 = 66.703125 (the remainder is 45, so 64 is not a divisor of 4269)
4269 / 65 = 65.676923076923 (the remainder is 44, so 65 is not a divisor of 4269)