What are the divisors of 4999?

1, 4999

There is a total of 2 positive divisors.
The sum of these divisors is 5000.
The arithmetic mean is 2500.

2 odd divisors

1, 4999

How to compute the divisors of 4999?

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 4999 by each of the numbers from 1 to 4999 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)

4999 / 1 = 4999 (the remainder is 0, so 1 is a divisor of 4999)
4999 / 2 = 2499.5 (the remainder is 1, so 2 is not a divisor of 4999)
4999 / 3 = 1666.3333333333 (the remainder is 1, so 3 is not a divisor of 4999)
...
4999 / 4998 = 1.000200080032 (the remainder is 1, so 4998 is not a divisor of 4999)
4999 / 4999 = 1 (the remainder is 0, so 4999 is a divisor of 4999)

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 4999 (i.e. 70.703606697254). 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 $\frac{N}{d} = D$ )

4999 / 1 = 4999 (the remainder is 0, so 1 and 4999 are divisors of 4999)
4999 / 2 = 2499.5 (the remainder is 1, so 2 is not a divisor of 4999)
4999 / 3 = 1666.3333333333 (the remainder is 1, so 3 is not a divisor of 4999)
...
4999 / 69 = 72.449275362319 (the remainder is 31, so 69 is not a divisor of 4999)
4999 / 70 = 71.414285714286 (the remainder is 29, so 70 is not a divisor of 4999)