What are the divisors of 4141?

1, 41, 101, 4141

There is a total of 4 positive divisors.
The sum of these divisors is 4284.
The arithmetic mean is 1071.

4 odd divisors

1, 41, 101, 4141

How to compute the divisors of 4141?

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 4141 by each of the numbers from 1 to 4141 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)

4141 / 1 = 4141 (the remainder is 0, so 1 is a divisor of 4141)
4141 / 2 = 2070.5 (the remainder is 1, so 2 is not a divisor of 4141)
4141 / 3 = 1380.3333333333 (the remainder is 1, so 3 is not a divisor of 4141)
...
4141 / 4140 = 1.0002415458937 (the remainder is 1, so 4140 is not a divisor of 4141)
4141 / 4141 = 1 (the remainder is 0, so 4141 is a divisor of 4141)

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 4141 (i.e. 64.350602172785). 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 $\frac{N}{d} = D$ )

4141 / 1 = 4141 (the remainder is 0, so 1 and 4141 are divisors of 4141)
4141 / 2 = 2070.5 (the remainder is 1, so 2 is not a divisor of 4141)
4141 / 3 = 1380.3333333333 (the remainder is 1, so 3 is not a divisor of 4141)
...
4141 / 63 = 65.730158730159 (the remainder is 46, so 63 is not a divisor of 4141)
4141 / 64 = 64.703125 (the remainder is 45, so 64 is not a divisor of 4141)