What are the divisors of 4267?

1, 17, 251, 4267

There is a total of 4 positive divisors.
The sum of these divisors is 4536.
The arithmetic mean is 1134.

4 odd divisors

1, 17, 251, 4267

How to compute the divisors of 4267?

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 4267 by each of the numbers from 1 to 4267 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)

4267 / 1 = 4267 (the remainder is 0, so 1 is a divisor of 4267)
4267 / 2 = 2133.5 (the remainder is 1, so 2 is not a divisor of 4267)
4267 / 3 = 1422.3333333333 (the remainder is 1, so 3 is not a divisor of 4267)
...
4267 / 4266 = 1.0002344116268 (the remainder is 1, so 4266 is not a divisor of 4267)
4267 / 4267 = 1 (the remainder is 0, so 4267 is a divisor of 4267)

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 4267 (i.e. 65.3222779762). 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 $\frac{N}{d} = D$ )

4267 / 1 = 4267 (the remainder is 0, so 1 and 4267 are divisors of 4267)
4267 / 2 = 2133.5 (the remainder is 1, so 2 is not a divisor of 4267)
4267 / 3 = 1422.3333333333 (the remainder is 1, so 3 is not a divisor of 4267)
...
4267 / 64 = 66.671875 (the remainder is 43, so 64 is not a divisor of 4267)
4267 / 65 = 65.646153846154 (the remainder is 42, so 65 is not a divisor of 4267)