What are the divisors of 5461?

1, 43, 127, 5461

There is a total of 4 positive divisors.
The sum of these divisors is 5632.
The arithmetic mean is 1408.

4 odd divisors

1, 43, 127, 5461

How to compute the divisors of 5461?

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 5461 by each of the numbers from 1 to 5461 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)

5461 / 1 = 5461 (the remainder is 0, so 1 is a divisor of 5461)
5461 / 2 = 2730.5 (the remainder is 1, so 2 is not a divisor of 5461)
5461 / 3 = 1820.3333333333 (the remainder is 1, so 3 is not a divisor of 5461)
...
5461 / 5460 = 1.0001831501832 (the remainder is 1, so 5460 is not a divisor of 5461)
5461 / 5461 = 1 (the remainder is 0, so 5461 is a divisor of 5461)

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 5461 (i.e. 73.898579147369). 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 $\frac{N}{d} = D$ )

5461 / 1 = 5461 (the remainder is 0, so 1 and 5461 are divisors of 5461)
5461 / 2 = 2730.5 (the remainder is 1, so 2 is not a divisor of 5461)
5461 / 3 = 1820.3333333333 (the remainder is 1, so 3 is not a divisor of 5461)
...
5461 / 72 = 75.847222222222 (the remainder is 61, so 72 is not a divisor of 5461)
5461 / 73 = 74.808219178082 (the remainder is 59, so 73 is not a divisor of 5461)