What are the divisors of 4496?

1, 2, 4, 8, 16, 281, 562, 1124, 2248, 4496

There is a total of 10 positive divisors.
The sum of these divisors is 8742.
The arithmetic mean is 874.2.

8 even divisors

2, 4, 8, 16, 562, 1124, 2248, 4496

2 odd divisors

1, 281

How to compute the divisors of 4496?

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 4496 by each of the numbers from 1 to 4496 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)

4496 / 1 = 4496 (the remainder is 0, so 1 is a divisor of 4496)
4496 / 2 = 2248 (the remainder is 0, so 2 is a divisor of 4496)
4496 / 3 = 1498.6666666667 (the remainder is 2, so 3 is not a divisor of 4496)
...
4496 / 4495 = 1.0002224694105 (the remainder is 1, so 4495 is not a divisor of 4496)
4496 / 4496 = 1 (the remainder is 0, so 4496 is a divisor of 4496)

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 4496 (i.e. 67.052218456961). 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 $\frac{N}{d} = D$ )

4496 / 1 = 4496 (the remainder is 0, so 1 and 4496 are divisors of 4496)
4496 / 2 = 2248 (the remainder is 0, so 2 and 2248 are divisors of 4496)
4496 / 3 = 1498.6666666667 (the remainder is 2, so 3 is not a divisor of 4496)
...
4496 / 66 = 68.121212121212 (the remainder is 8, so 66 is not a divisor of 4496)
4496 / 67 = 67.10447761194 (the remainder is 7, so 67 is not a divisor of 4496)