What are the divisors of 4103?

1, 11, 373, 4103

There is a total of 4 positive divisors.
The sum of these divisors is 4488.
The arithmetic mean is 1122.

4 odd divisors

1, 11, 373, 4103

How to compute the divisors of 4103?

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 4103 by each of the numbers from 1 to 4103 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)

4103 / 1 = 4103 (the remainder is 0, so 1 is a divisor of 4103)
4103 / 2 = 2051.5 (the remainder is 1, so 2 is not a divisor of 4103)
4103 / 3 = 1367.6666666667 (the remainder is 2, so 3 is not a divisor of 4103)
...
4103 / 4102 = 1.0002437835202 (the remainder is 1, so 4102 is not a divisor of 4103)
4103 / 4103 = 1 (the remainder is 0, so 4103 is a divisor of 4103)

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 4103 (i.e. 64.054664154923). 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 $\frac{N}{d} = D$ )

4103 / 1 = 4103 (the remainder is 0, so 1 and 4103 are divisors of 4103)
4103 / 2 = 2051.5 (the remainder is 1, so 2 is not a divisor of 4103)
4103 / 3 = 1367.6666666667 (the remainder is 2, so 3 is not a divisor of 4103)
...
4103 / 63 = 65.126984126984 (the remainder is 8, so 63 is not a divisor of 4103)
4103 / 64 = 64.109375 (the remainder is 7, so 64 is not a divisor of 4103)