What are the divisors of 5476?

1, 2, 4, 37, 74, 148, 1369, 2738, 5476

There is a total of 9 positive divisors.
The sum of these divisors is 9849.
The arithmetic mean is 1094.3333333333.

6 even divisors

2, 4, 74, 148, 2738, 5476

3 odd divisors

1, 37, 1369

How to compute the divisors of 5476?

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 5476 by each of the numbers from 1 to 5476 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)

5476 / 1 = 5476 (the remainder is 0, so 1 is a divisor of 5476)
5476 / 2 = 2738 (the remainder is 0, so 2 is a divisor of 5476)
5476 / 3 = 1825.3333333333 (the remainder is 1, so 3 is not a divisor of 5476)
...
5476 / 5475 = 1.0001826484018 (the remainder is 1, so 5475 is not a divisor of 5476)
5476 / 5476 = 1 (the remainder is 0, so 5476 is a divisor of 5476)

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 5476 (i.e. 74). 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 $\frac{N}{d} = D$ )

5476 / 1 = 5476 (the remainder is 0, so 1 and 5476 are divisors of 5476)
5476 / 2 = 2738 (the remainder is 0, so 2 and 2738 are divisors of 5476)
5476 / 3 = 1825.3333333333 (the remainder is 1, so 3 is not a divisor of 5476)
...
5476 / 73 = 75.013698630137 (the remainder is 1, so 73 is not a divisor of 5476)
5476 / 74 = 74 (the remainder is 0, so 74 and 74 are divisors of 5476)