What are the divisors of 4293?

1, 3, 9, 27, 53, 81, 159, 477, 1431, 4293

There is a total of 10 positive divisors.
The sum of these divisors is 6534.
The arithmetic mean is 653.4.

10 odd divisors

1, 3, 9, 27, 53, 81, 159, 477, 1431, 4293

How to compute the divisors of 4293?

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 4293 by each of the numbers from 1 to 4293 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)

4293 / 1 = 4293 (the remainder is 0, so 1 is a divisor of 4293)
4293 / 2 = 2146.5 (the remainder is 1, so 2 is not a divisor of 4293)
4293 / 3 = 1431 (the remainder is 0, so 3 is a divisor of 4293)
...
4293 / 4292 = 1.0002329916123 (the remainder is 1, so 4292 is not a divisor of 4293)
4293 / 4293 = 1 (the remainder is 0, so 4293 is a divisor of 4293)

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 4293 (i.e. 65.520989003525). 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 $\frac{N}{d} = D$ )

4293 / 1 = 4293 (the remainder is 0, so 1 and 4293 are divisors of 4293)
4293 / 2 = 2146.5 (the remainder is 1, so 2 is not a divisor of 4293)
4293 / 3 = 1431 (the remainder is 0, so 3 and 1431 are divisors of 4293)
...
4293 / 64 = 67.078125 (the remainder is 5, so 64 is not a divisor of 4293)
4293 / 65 = 66.046153846154 (the remainder is 3, so 65 is not a divisor of 4293)