What are the divisors of 5434?

1, 2, 11, 13, 19, 22, 26, 38, 143, 209, 247, 286, 418, 494, 2717, 5434

There is a total of 16 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 630.

8 even divisors

2, 22, 26, 38, 286, 418, 494, 5434

8 odd divisors

1, 11, 13, 19, 143, 209, 247, 2717

How to compute the divisors of 5434?

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 5434 by each of the numbers from 1 to 5434 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)

5434 / 1 = 5434 (the remainder is 0, so 1 is a divisor of 5434)
5434 / 2 = 2717 (the remainder is 0, so 2 is a divisor of 5434)
5434 / 3 = 1811.3333333333 (the remainder is 1, so 3 is not a divisor of 5434)
...
5434 / 5433 = 1.0001840603718 (the remainder is 1, so 5433 is not a divisor of 5434)
5434 / 5434 = 1 (the remainder is 0, so 5434 is a divisor of 5434)

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 5434 (i.e. 73.715669975928). 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 $\frac{N}{d} = D$ )

5434 / 1 = 5434 (the remainder is 0, so 1 and 5434 are divisors of 5434)
5434 / 2 = 2717 (the remainder is 0, so 2 and 2717 are divisors of 5434)
5434 / 3 = 1811.3333333333 (the remainder is 1, so 3 is not a divisor of 5434)
...
5434 / 72 = 75.472222222222 (the remainder is 34, so 72 is not a divisor of 5434)
5434 / 73 = 74.438356164384 (the remainder is 32, so 73 is not a divisor of 5434)