What are the divisors of 4987?

1, 4987

There is a total of 2 positive divisors.
The sum of these divisors is 4988.
The arithmetic mean is 2494.

2 odd divisors

1, 4987

How to compute the divisors of 4987?

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 4987 by each of the numbers from 1 to 4987 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)

4987 / 1 = 4987 (the remainder is 0, so 1 is a divisor of 4987)
4987 / 2 = 2493.5 (the remainder is 1, so 2 is not a divisor of 4987)
4987 / 3 = 1662.3333333333 (the remainder is 1, so 3 is not a divisor of 4987)
...
4987 / 4986 = 1.0002005615724 (the remainder is 1, so 4986 is not a divisor of 4987)
4987 / 4987 = 1 (the remainder is 0, so 4987 is a divisor of 4987)

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 4987 (i.e. 70.618694408775). 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 $\frac{N}{d} = D$ )

4987 / 1 = 4987 (the remainder is 0, so 1 and 4987 are divisors of 4987)
4987 / 2 = 2493.5 (the remainder is 1, so 2 is not a divisor of 4987)
4987 / 3 = 1662.3333333333 (the remainder is 1, so 3 is not a divisor of 4987)
...
4987 / 69 = 72.275362318841 (the remainder is 19, so 69 is not a divisor of 4987)
4987 / 70 = 71.242857142857 (the remainder is 17, so 70 is not a divisor of 4987)