What are the divisors of 2195?

1, 5, 439, 2195

There is a total of 4 positive divisors.
The sum of these divisors is 2640.
The arithmetic mean is 660.

4 odd divisors

1, 5, 439, 2195

How to compute the divisors of 2195?

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 2195 by each of the numbers from 1 to 2195 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)

2195 / 1 = 2195 (the remainder is 0, so 1 is a divisor of 2195)
2195 / 2 = 1097.5 (the remainder is 1, so 2 is not a divisor of 2195)
2195 / 3 = 731.66666666667 (the remainder is 2, so 3 is not a divisor of 2195)
...
2195 / 2194 = 1.0004557885141 (the remainder is 1, so 2194 is not a divisor of 2195)
2195 / 2195 = 1 (the remainder is 0, so 2195 is a divisor of 2195)

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 2195 (i.e. 46.85082710049). 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 $\frac{N}{d} = D$ )

2195 / 1 = 2195 (the remainder is 0, so 1 and 2195 are divisors of 2195)
2195 / 2 = 1097.5 (the remainder is 1, so 2 is not a divisor of 2195)
2195 / 3 = 731.66666666667 (the remainder is 2, so 3 is not a divisor of 2195)
...
2195 / 45 = 48.777777777778 (the remainder is 35, so 45 is not a divisor of 2195)
2195 / 46 = 47.717391304348 (the remainder is 33, so 46 is not a divisor of 2195)