What are the divisors of 5495?

1, 5, 7, 35, 157, 785, 1099, 5495

There is a total of 8 positive divisors.
The sum of these divisors is 7584.
The arithmetic mean is 948.

8 odd divisors

1, 5, 7, 35, 157, 785, 1099, 5495

How to compute the divisors of 5495?

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 5495 by each of the numbers from 1 to 5495 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)

5495 / 1 = 5495 (the remainder is 0, so 1 is a divisor of 5495)
5495 / 2 = 2747.5 (the remainder is 1, so 2 is not a divisor of 5495)
5495 / 3 = 1831.6666666667 (the remainder is 2, so 3 is not a divisor of 5495)
...
5495 / 5494 = 1.0001820167455 (the remainder is 1, so 5494 is not a divisor of 5495)
5495 / 5495 = 1 (the remainder is 0, so 5495 is a divisor of 5495)

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 5495 (i.e. 74.128267212987). 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 $\frac{N}{d} = D$ )

5495 / 1 = 5495 (the remainder is 0, so 1 and 5495 are divisors of 5495)
5495 / 2 = 2747.5 (the remainder is 1, so 2 is not a divisor of 5495)
5495 / 3 = 1831.6666666667 (the remainder is 2, so 3 is not a divisor of 5495)
...
5495 / 73 = 75.27397260274 (the remainder is 20, so 73 is not a divisor of 5495)
5495 / 74 = 74.256756756757 (the remainder is 19, so 74 is not a divisor of 5495)