What are the divisors of 4241?

1, 4241

There is a total of 2 positive divisors.
The sum of these divisors is 4242.
The arithmetic mean is 2121.

2 odd divisors

1, 4241

How to compute the divisors of 4241?

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 4241 by each of the numbers from 1 to 4241 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)

4241 / 1 = 4241 (the remainder is 0, so 1 is a divisor of 4241)
4241 / 2 = 2120.5 (the remainder is 1, so 2 is not a divisor of 4241)
4241 / 3 = 1413.6666666667 (the remainder is 2, so 3 is not a divisor of 4241)
...
4241 / 4240 = 1.0002358490566 (the remainder is 1, so 4240 is not a divisor of 4241)
4241 / 4241 = 1 (the remainder is 0, so 4241 is a divisor of 4241)

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 4241 (i.e. 65.12296062066). 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 $\frac{N}{d} = D$ )

4241 / 1 = 4241 (the remainder is 0, so 1 and 4241 are divisors of 4241)
4241 / 2 = 2120.5 (the remainder is 1, so 2 is not a divisor of 4241)
4241 / 3 = 1413.6666666667 (the remainder is 2, so 3 is not a divisor of 4241)
...
4241 / 64 = 66.265625 (the remainder is 17, so 64 is not a divisor of 4241)
4241 / 65 = 65.246153846154 (the remainder is 16, so 65 is not a divisor of 4241)