What are the divisors of 5451?

1, 3, 23, 69, 79, 237, 1817, 5451

There is a total of 8 positive divisors.
The sum of these divisors is 7680.
The arithmetic mean is 960.

8 odd divisors

1, 3, 23, 69, 79, 237, 1817, 5451

How to compute the divisors of 5451?

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 5451 by each of the numbers from 1 to 5451 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)

5451 / 1 = 5451 (the remainder is 0, so 1 is a divisor of 5451)
5451 / 2 = 2725.5 (the remainder is 1, so 2 is not a divisor of 5451)
5451 / 3 = 1817 (the remainder is 0, so 3 is a divisor of 5451)
...
5451 / 5450 = 1.0001834862385 (the remainder is 1, so 5450 is not a divisor of 5451)
5451 / 5451 = 1 (the remainder is 0, so 5451 is a divisor of 5451)

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 5451 (i.e. 73.830887845129). 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 $\frac{N}{d} = D$ )

5451 / 1 = 5451 (the remainder is 0, so 1 and 5451 are divisors of 5451)
5451 / 2 = 2725.5 (the remainder is 1, so 2 is not a divisor of 5451)
5451 / 3 = 1817 (the remainder is 0, so 3 and 1817 are divisors of 5451)
...
5451 / 72 = 75.708333333333 (the remainder is 51, so 72 is not a divisor of 5451)
5451 / 73 = 74.671232876712 (the remainder is 49, so 73 is not a divisor of 5451)