What are the divisors of 5429?

1, 61, 89, 5429

There is a total of 4 positive divisors.
The sum of these divisors is 5580.
The arithmetic mean is 1395.

4 odd divisors

1, 61, 89, 5429

How to compute the divisors of 5429?

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 5429 by each of the numbers from 1 to 5429 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)

5429 / 1 = 5429 (the remainder is 0, so 1 is a divisor of 5429)
5429 / 2 = 2714.5 (the remainder is 1, so 2 is not a divisor of 5429)
5429 / 3 = 1809.6666666667 (the remainder is 2, so 3 is not a divisor of 5429)
...
5429 / 5428 = 1.0001842299189 (the remainder is 1, so 5428 is not a divisor of 5429)
5429 / 5429 = 1 (the remainder is 0, so 5429 is a divisor of 5429)

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 5429 (i.e. 73.681748079155). 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 $\frac{N}{d} = D$ )

5429 / 1 = 5429 (the remainder is 0, so 1 and 5429 are divisors of 5429)
5429 / 2 = 2714.5 (the remainder is 1, so 2 is not a divisor of 5429)
5429 / 3 = 1809.6666666667 (the remainder is 2, so 3 is not a divisor of 5429)
...
5429 / 72 = 75.402777777778 (the remainder is 29, so 72 is not a divisor of 5429)
5429 / 73 = 74.369863013699 (the remainder is 27, so 73 is not a divisor of 5429)