What are the divisors of 4173?

1, 3, 13, 39, 107, 321, 1391, 4173

There is a total of 8 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 756.

8 odd divisors

1, 3, 13, 39, 107, 321, 1391, 4173

How to compute the divisors of 4173?

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 4173 by each of the numbers from 1 to 4173 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)

4173 / 1 = 4173 (the remainder is 0, so 1 is a divisor of 4173)
4173 / 2 = 2086.5 (the remainder is 1, so 2 is not a divisor of 4173)
4173 / 3 = 1391 (the remainder is 0, so 3 is a divisor of 4173)
...
4173 / 4172 = 1.0002396931927 (the remainder is 1, so 4172 is not a divisor of 4173)
4173 / 4173 = 1 (the remainder is 0, so 4173 is a divisor of 4173)

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 4173 (i.e. 64.598761598037). 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 $\frac{N}{d} = D$ )

4173 / 1 = 4173 (the remainder is 0, so 1 and 4173 are divisors of 4173)
4173 / 2 = 2086.5 (the remainder is 1, so 2 is not a divisor of 4173)
4173 / 3 = 1391 (the remainder is 0, so 3 and 1391 are divisors of 4173)
...
4173 / 63 = 66.238095238095 (the remainder is 15, so 63 is not a divisor of 4173)
4173 / 64 = 65.203125 (the remainder is 13, so 64 is not a divisor of 4173)