What are the divisors of 995?

1, 5, 199, 995

There is a total of 4 positive divisors.
The sum of these divisors is 1200.
The arithmetic mean is 300.

4 odd divisors

1, 5, 199, 995

How to compute the divisors of 995?

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 995 by each of the numbers from 1 to 995 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)

995 / 1 = 995 (the remainder is 0, so 1 is a divisor of 995)
995 / 2 = 497.5 (the remainder is 1, so 2 is not a divisor of 995)
995 / 3 = 331.66666666667 (the remainder is 2, so 3 is not a divisor of 995)
...
995 / 994 = 1.0010060362173 (the remainder is 1, so 994 is not a divisor of 995)
995 / 995 = 1 (the remainder is 0, so 995 is a divisor of 995)

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 995 (i.e. 31.543620591175). 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 $\frac{N}{d} = D$ )

995 / 1 = 995 (the remainder is 0, so 1 and 995 are divisors of 995)
995 / 2 = 497.5 (the remainder is 1, so 2 is not a divisor of 995)
995 / 3 = 331.66666666667 (the remainder is 2, so 3 is not a divisor of 995)
...
995 / 30 = 33.166666666667 (the remainder is 5, so 30 is not a divisor of 995)
995 / 31 = 32.096774193548 (the remainder is 3, so 31 is not a divisor of 995)