What are the divisors of 5457?

1, 3, 17, 51, 107, 321, 1819, 5457

There is a total of 8 positive divisors.
The sum of these divisors is 7776.
The arithmetic mean is 972.

8 odd divisors

1, 3, 17, 51, 107, 321, 1819, 5457

How to compute the divisors of 5457?

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 5457 by each of the numbers from 1 to 5457 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)

5457 / 1 = 5457 (the remainder is 0, so 1 is a divisor of 5457)
5457 / 2 = 2728.5 (the remainder is 1, so 2 is not a divisor of 5457)
5457 / 3 = 1819 (the remainder is 0, so 3 is a divisor of 5457)
...
5457 / 5456 = 1.0001832844575 (the remainder is 1, so 5456 is not a divisor of 5457)
5457 / 5457 = 1 (the remainder is 0, so 5457 is a divisor of 5457)

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 5457 (i.e. 73.87151006985). 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 $\frac{N}{d} = D$ )

5457 / 1 = 5457 (the remainder is 0, so 1 and 5457 are divisors of 5457)
5457 / 2 = 2728.5 (the remainder is 1, so 2 is not a divisor of 5457)
5457 / 3 = 1819 (the remainder is 0, so 3 and 1819 are divisors of 5457)
...
5457 / 72 = 75.791666666667 (the remainder is 57, so 72 is not a divisor of 5457)
5457 / 73 = 74.753424657534 (the remainder is 55, so 73 is not a divisor of 5457)