What are the divisors of 5452?

1, 2, 4, 29, 47, 58, 94, 116, 188, 1363, 2726, 5452

There is a total of 12 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 840.

8 even divisors

2, 4, 58, 94, 116, 188, 2726, 5452

4 odd divisors

1, 29, 47, 1363

How to compute the divisors of 5452?

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 5452 by each of the numbers from 1 to 5452 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)

5452 / 1 = 5452 (the remainder is 0, so 1 is a divisor of 5452)
5452 / 2 = 2726 (the remainder is 0, so 2 is a divisor of 5452)
5452 / 3 = 1817.3333333333 (the remainder is 1, so 3 is not a divisor of 5452)
...
5452 / 5451 = 1.0001834525775 (the remainder is 1, so 5451 is not a divisor of 5452)
5452 / 5452 = 1 (the remainder is 0, so 5452 is a divisor of 5452)

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 5452 (i.e. 73.837659767899). 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 $\frac{N}{d} = D$ )

5452 / 1 = 5452 (the remainder is 0, so 1 and 5452 are divisors of 5452)
5452 / 2 = 2726 (the remainder is 0, so 2 and 2726 are divisors of 5452)
5452 / 3 = 1817.3333333333 (the remainder is 1, so 3 is not a divisor of 5452)
...
5452 / 72 = 75.722222222222 (the remainder is 52, so 72 is not a divisor of 5452)
5452 / 73 = 74.684931506849 (the remainder is 50, so 73 is not a divisor of 5452)