What are the divisors of 4261?

1, 4261

There is a total of 2 positive divisors.
The sum of these divisors is 4262.
The arithmetic mean is 2131.

2 odd divisors

1, 4261

How to compute the divisors of 4261?

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 4261 by each of the numbers from 1 to 4261 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)

4261 / 1 = 4261 (the remainder is 0, so 1 is a divisor of 4261)
4261 / 2 = 2130.5 (the remainder is 1, so 2 is not a divisor of 4261)
4261 / 3 = 1420.3333333333 (the remainder is 1, so 3 is not a divisor of 4261)
...
4261 / 4260 = 1.000234741784 (the remainder is 1, so 4260 is not a divisor of 4261)
4261 / 4261 = 1 (the remainder is 0, so 4261 is a divisor of 4261)

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 4261 (i.e. 65.27633568147). 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 $\frac{N}{d} = D$ )

4261 / 1 = 4261 (the remainder is 0, so 1 and 4261 are divisors of 4261)
4261 / 2 = 2130.5 (the remainder is 1, so 2 is not a divisor of 4261)
4261 / 3 = 1420.3333333333 (the remainder is 1, so 3 is not a divisor of 4261)
...
4261 / 64 = 66.578125 (the remainder is 37, so 64 is not a divisor of 4261)
4261 / 65 = 65.553846153846 (the remainder is 36, so 65 is not a divisor of 4261)