What are the divisors of 4288?

1, 2, 4, 8, 16, 32, 64, 67, 134, 268, 536, 1072, 2144, 4288

There is a total of 14 positive divisors.
The sum of these divisors is 8636.
The arithmetic mean is 616.85714285714.

12 even divisors

2, 4, 8, 16, 32, 64, 134, 268, 536, 1072, 2144, 4288

2 odd divisors

1, 67

How to compute the divisors of 4288?

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 4288 by each of the numbers from 1 to 4288 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)

4288 / 1 = 4288 (the remainder is 0, so 1 is a divisor of 4288)
4288 / 2 = 2144 (the remainder is 0, so 2 is a divisor of 4288)
4288 / 3 = 1429.3333333333 (the remainder is 1, so 3 is not a divisor of 4288)
...
4288 / 4287 = 1.0002332633543 (the remainder is 1, so 4287 is not a divisor of 4288)
4288 / 4288 = 1 (the remainder is 0, so 4288 is a divisor of 4288)

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 4288 (i.e. 65.48282217498). 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 $\frac{N}{d} = D$ )

4288 / 1 = 4288 (the remainder is 0, so 1 and 4288 are divisors of 4288)
4288 / 2 = 2144 (the remainder is 0, so 2 and 2144 are divisors of 4288)
4288 / 3 = 1429.3333333333 (the remainder is 1, so 3 is not a divisor of 4288)
...
4288 / 64 = 67 (the remainder is 0, so 64 and 67 are divisors of 4288)
4288 / 65 = 65.969230769231 (the remainder is 63, so 65 is not a divisor of 4288)