What are the divisors of 4492?

1, 2, 4, 1123, 2246, 4492

There is a total of 6 positive divisors.
The sum of these divisors is 7868.
The arithmetic mean is 1311.3333333333.

4 even divisors

2, 4, 2246, 4492

2 odd divisors

1, 1123

How to compute the divisors of 4492?

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 4492 by each of the numbers from 1 to 4492 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)

4492 / 1 = 4492 (the remainder is 0, so 1 is a divisor of 4492)
4492 / 2 = 2246 (the remainder is 0, so 2 is a divisor of 4492)
4492 / 3 = 1497.3333333333 (the remainder is 1, so 3 is not a divisor of 4492)
...
4492 / 4491 = 1.0002226675573 (the remainder is 1, so 4491 is not a divisor of 4492)
4492 / 4492 = 1 (the remainder is 0, so 4492 is a divisor of 4492)

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 4492 (i.e. 67.022384320464). 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 $\frac{N}{d} = D$ )

4492 / 1 = 4492 (the remainder is 0, so 1 and 4492 are divisors of 4492)
4492 / 2 = 2246 (the remainder is 0, so 2 and 2246 are divisors of 4492)
4492 / 3 = 1497.3333333333 (the remainder is 1, so 3 is not a divisor of 4492)
...
4492 / 66 = 68.060606060606 (the remainder is 4, so 66 is not a divisor of 4492)
4492 / 67 = 67.044776119403 (the remainder is 3, so 67 is not a divisor of 4492)