What are the divisors of 5615?

1, 5, 1123, 5615

There is a total of 4 positive divisors.
The sum of these divisors is 6744.
The arithmetic mean is 1686.

4 odd divisors

1, 5, 1123, 5615

How to compute the divisors of 5615?

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 5615 by each of the numbers from 1 to 5615 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)

5615 / 1 = 5615 (the remainder is 0, so 1 is a divisor of 5615)
5615 / 2 = 2807.5 (the remainder is 1, so 2 is not a divisor of 5615)
5615 / 3 = 1871.6666666667 (the remainder is 2, so 3 is not a divisor of 5615)
...
5615 / 5614 = 1.0001781261133 (the remainder is 1, so 5614 is not a divisor of 5615)
5615 / 5615 = 1 (the remainder is 0, so 5615 is a divisor of 5615)

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 5615 (i.e. 74.933303677337). 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 $\frac{N}{d} = D$ )

5615 / 1 = 5615 (the remainder is 0, so 1 and 5615 are divisors of 5615)
5615 / 2 = 2807.5 (the remainder is 1, so 2 is not a divisor of 5615)
5615 / 3 = 1871.6666666667 (the remainder is 2, so 3 is not a divisor of 5615)
...
5615 / 73 = 76.917808219178 (the remainder is 67, so 73 is not a divisor of 5615)
5615 / 74 = 75.878378378378 (the remainder is 65, so 74 is not a divisor of 5615)