What are the divisors of 5414?

1, 2, 2707, 5414

There is a total of 4 positive divisors.
The sum of these divisors is 8124.
The arithmetic mean is 2031.

2 even divisors

2, 5414

2 odd divisors

1, 2707

How to compute the divisors of 5414?

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 5414 by each of the numbers from 1 to 5414 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)

5414 / 1 = 5414 (the remainder is 0, so 1 is a divisor of 5414)
5414 / 2 = 2707 (the remainder is 0, so 2 is a divisor of 5414)
5414 / 3 = 1804.6666666667 (the remainder is 2, so 3 is not a divisor of 5414)
...
5414 / 5413 = 1.0001847404397 (the remainder is 1, so 5413 is not a divisor of 5414)
5414 / 5414 = 1 (the remainder is 0, so 5414 is a divisor of 5414)

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 5414 (i.e. 73.579888556589). 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 $\frac{N}{d} = D$ )

5414 / 1 = 5414 (the remainder is 0, so 1 and 5414 are divisors of 5414)
5414 / 2 = 2707 (the remainder is 0, so 2 and 2707 are divisors of 5414)
5414 / 3 = 1804.6666666667 (the remainder is 2, so 3 is not a divisor of 5414)
...
5414 / 72 = 75.194444444444 (the remainder is 14, so 72 is not a divisor of 5414)
5414 / 73 = 74.164383561644 (the remainder is 12, so 73 is not a divisor of 5414)