What are the divisors of 4171?

1, 43, 97, 4171

There is a total of 4 positive divisors.
The sum of these divisors is 4312.
The arithmetic mean is 1078.

4 odd divisors

1, 43, 97, 4171

How to compute the divisors of 4171?

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 4171 by each of the numbers from 1 to 4171 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)

4171 / 1 = 4171 (the remainder is 0, so 1 is a divisor of 4171)
4171 / 2 = 2085.5 (the remainder is 1, so 2 is not a divisor of 4171)
4171 / 3 = 1390.3333333333 (the remainder is 1, so 3 is not a divisor of 4171)
...
4171 / 4170 = 1.0002398081535 (the remainder is 1, so 4170 is not a divisor of 4171)
4171 / 4171 = 1 (the remainder is 0, so 4171 is a divisor of 4171)

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 4171 (i.e. 64.58327956987). 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 $\frac{N}{d} = D$ )

4171 / 1 = 4171 (the remainder is 0, so 1 and 4171 are divisors of 4171)
4171 / 2 = 2085.5 (the remainder is 1, so 2 is not a divisor of 4171)
4171 / 3 = 1390.3333333333 (the remainder is 1, so 3 is not a divisor of 4171)
...
4171 / 63 = 66.206349206349 (the remainder is 13, so 63 is not a divisor of 4171)
4171 / 64 = 65.171875 (the remainder is 11, so 64 is not a divisor of 4171)