What are the divisors of 5482?

1, 2, 2741, 5482

There is a total of 4 positive divisors.
The sum of these divisors is 8226.
The arithmetic mean is 2056.5.

2 even divisors

2, 5482

2 odd divisors

1, 2741

How to compute the divisors of 5482?

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 5482 by each of the numbers from 1 to 5482 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)

5482 / 1 = 5482 (the remainder is 0, so 1 is a divisor of 5482)
5482 / 2 = 2741 (the remainder is 0, so 2 is a divisor of 5482)
5482 / 3 = 1827.3333333333 (the remainder is 1, so 3 is not a divisor of 5482)
...
5482 / 5481 = 1.0001824484583 (the remainder is 1, so 5481 is not a divisor of 5482)
5482 / 5482 = 1 (the remainder is 0, so 5482 is a divisor of 5482)

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 5482 (i.e. 74.040529441651). 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 $\frac{N}{d} = D$ )

5482 / 1 = 5482 (the remainder is 0, so 1 and 5482 are divisors of 5482)
5482 / 2 = 2741 (the remainder is 0, so 2 and 2741 are divisors of 5482)
5482 / 3 = 1827.3333333333 (the remainder is 1, so 3 is not a divisor of 5482)
...
5482 / 73 = 75.095890410959 (the remainder is 7, so 73 is not a divisor of 5482)
5482 / 74 = 74.081081081081 (the remainder is 6, so 74 is not a divisor of 5482)