What are the divisors of 2995?

1, 5, 599, 2995

There is a total of 4 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 900.

4 odd divisors

1, 5, 599, 2995

How to compute the divisors of 2995?

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 2995 by each of the numbers from 1 to 2995 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)

2995 / 1 = 2995 (the remainder is 0, so 1 is a divisor of 2995)
2995 / 2 = 1497.5 (the remainder is 1, so 2 is not a divisor of 2995)
2995 / 3 = 998.33333333333 (the remainder is 1, so 3 is not a divisor of 2995)
...
2995 / 2994 = 1.000334001336 (the remainder is 1, so 2994 is not a divisor of 2995)
2995 / 2995 = 1 (the remainder is 0, so 2995 is a divisor of 2995)

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 2995 (i.e. 54.726593170049). 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 $\frac{N}{d} = D$ )

2995 / 1 = 2995 (the remainder is 0, so 1 and 2995 are divisors of 2995)
2995 / 2 = 1497.5 (the remainder is 1, so 2 is not a divisor of 2995)
2995 / 3 = 998.33333333333 (the remainder is 1, so 3 is not a divisor of 2995)
...
2995 / 53 = 56.509433962264 (the remainder is 27, so 53 is not a divisor of 2995)
2995 / 54 = 55.462962962963 (the remainder is 25, so 54 is not a divisor of 2995)