What are the divisors of 4257?

1, 3, 9, 11, 33, 43, 99, 129, 387, 473, 1419, 4257

There is a total of 12 positive divisors.
The sum of these divisors is 6864.
The arithmetic mean is 572.

12 odd divisors

1, 3, 9, 11, 33, 43, 99, 129, 387, 473, 1419, 4257

How to compute the divisors of 4257?

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 4257 by each of the numbers from 1 to 4257 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)

4257 / 1 = 4257 (the remainder is 0, so 1 is a divisor of 4257)
4257 / 2 = 2128.5 (the remainder is 1, so 2 is not a divisor of 4257)
4257 / 3 = 1419 (the remainder is 0, so 3 is a divisor of 4257)
...
4257 / 4256 = 1.000234962406 (the remainder is 1, so 4256 is not a divisor of 4257)
4257 / 4257 = 1 (the remainder is 0, so 4257 is a divisor of 4257)

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 4257 (i.e. 65.245689512795). 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 $\frac{N}{d} = D$ )

4257 / 1 = 4257 (the remainder is 0, so 1 and 4257 are divisors of 4257)
4257 / 2 = 2128.5 (the remainder is 1, so 2 is not a divisor of 4257)
4257 / 3 = 1419 (the remainder is 0, so 3 and 1419 are divisors of 4257)
...
4257 / 64 = 66.515625 (the remainder is 33, so 64 is not a divisor of 4257)
4257 / 65 = 65.492307692308 (the remainder is 32, so 65 is not a divisor of 4257)