What are the divisors of 5462?

1, 2, 2731, 5462

There is a total of 4 positive divisors.
The sum of these divisors is 8196.
The arithmetic mean is 2049.

2 even divisors

2, 5462

2 odd divisors

1, 2731

How to compute the divisors of 5462?

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 5462 by each of the numbers from 1 to 5462 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)

5462 / 1 = 5462 (the remainder is 0, so 1 is a divisor of 5462)
5462 / 2 = 2731 (the remainder is 0, so 2 is a divisor of 5462)
5462 / 3 = 1820.6666666667 (the remainder is 2, so 3 is not a divisor of 5462)
...
5462 / 5461 = 1.0001831166453 (the remainder is 1, so 5461 is not a divisor of 5462)
5462 / 5462 = 1 (the remainder is 0, so 5462 is a divisor of 5462)

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 5462 (i.e. 73.905344867608). 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 $\frac{N}{d} = D$ )

5462 / 1 = 5462 (the remainder is 0, so 1 and 5462 are divisors of 5462)
5462 / 2 = 2731 (the remainder is 0, so 2 and 2731 are divisors of 5462)
5462 / 3 = 1820.6666666667 (the remainder is 2, so 3 is not a divisor of 5462)
...
5462 / 72 = 75.861111111111 (the remainder is 62, so 72 is not a divisor of 5462)
5462 / 73 = 74.821917808219 (the remainder is 60, so 73 is not a divisor of 5462)