What are the divisors of 4193?

1, 7, 599, 4193

There is a total of 4 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 1200.

4 odd divisors

1, 7, 599, 4193

How to compute the divisors of 4193?

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 4193 by each of the numbers from 1 to 4193 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)

4193 / 1 = 4193 (the remainder is 0, so 1 is a divisor of 4193)
4193 / 2 = 2096.5 (the remainder is 1, so 2 is not a divisor of 4193)
4193 / 3 = 1397.6666666667 (the remainder is 2, so 3 is not a divisor of 4193)
...
4193 / 4192 = 1.0002385496183 (the remainder is 1, so 4192 is not a divisor of 4193)
4193 / 4193 = 1 (the remainder is 0, so 4193 is a divisor of 4193)

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 4193 (i.e. 64.753378290248). 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 $\frac{N}{d} = D$ )

4193 / 1 = 4193 (the remainder is 0, so 1 and 4193 are divisors of 4193)
4193 / 2 = 2096.5 (the remainder is 1, so 2 is not a divisor of 4193)
4193 / 3 = 1397.6666666667 (the remainder is 2, so 3 is not a divisor of 4193)
...
4193 / 63 = 66.555555555556 (the remainder is 35, so 63 is not a divisor of 4193)
4193 / 64 = 65.515625 (the remainder is 33, so 64 is not a divisor of 4193)