What are the divisors of 4264?

1, 2, 4, 8, 13, 26, 41, 52, 82, 104, 164, 328, 533, 1066, 2132, 4264

There is a total of 16 positive divisors.
The sum of these divisors is 8820.
The arithmetic mean is 551.25.

12 even divisors

2, 4, 8, 26, 52, 82, 104, 164, 328, 1066, 2132, 4264

4 odd divisors

1, 13, 41, 533

How to compute the divisors of 4264?

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 4264 by each of the numbers from 1 to 4264 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)

4264 / 1 = 4264 (the remainder is 0, so 1 is a divisor of 4264)
4264 / 2 = 2132 (the remainder is 0, so 2 is a divisor of 4264)
4264 / 3 = 1421.3333333333 (the remainder is 1, so 3 is not a divisor of 4264)
...
4264 / 4263 = 1.0002345765893 (the remainder is 1, so 4263 is not a divisor of 4264)
4264 / 4264 = 1 (the remainder is 0, so 4264 is a divisor of 4264)

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 4264 (i.e. 65.299310869258). 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 $\frac{N}{d} = D$ )

4264 / 1 = 4264 (the remainder is 0, so 1 and 4264 are divisors of 4264)
4264 / 2 = 2132 (the remainder is 0, so 2 and 2132 are divisors of 4264)
4264 / 3 = 1421.3333333333 (the remainder is 1, so 3 is not a divisor of 4264)
...
4264 / 64 = 66.625 (the remainder is 40, so 64 is not a divisor of 4264)
4264 / 65 = 65.6 (the remainder is 39, so 65 is not a divisor of 4264)