What are the divisors of 4265?

1, 5, 853, 4265

There is a total of 4 positive divisors.
The sum of these divisors is 5124.
The arithmetic mean is 1281.

4 odd divisors

1, 5, 853, 4265

How to compute the divisors of 4265?

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 4265 by each of the numbers from 1 to 4265 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)

4265 / 1 = 4265 (the remainder is 0, so 1 is a divisor of 4265)
4265 / 2 = 2132.5 (the remainder is 1, so 2 is not a divisor of 4265)
4265 / 3 = 1421.6666666667 (the remainder is 2, so 3 is not a divisor of 4265)
...
4265 / 4264 = 1.000234521576 (the remainder is 1, so 4264 is not a divisor of 4265)
4265 / 4265 = 1 (the remainder is 0, so 4265 is a divisor of 4265)

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 4265 (i.e. 65.306967469023). 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 $\frac{N}{d} = D$ )

4265 / 1 = 4265 (the remainder is 0, so 1 and 4265 are divisors of 4265)
4265 / 2 = 2132.5 (the remainder is 1, so 2 is not a divisor of 4265)
4265 / 3 = 1421.6666666667 (the remainder is 2, so 3 is not a divisor of 4265)
...
4265 / 64 = 66.640625 (the remainder is 41, so 64 is not a divisor of 4265)
4265 / 65 = 65.615384615385 (the remainder is 40, so 65 is not a divisor of 4265)