What are the divisors of 4487?

1, 7, 641, 4487

There is a total of 4 positive divisors.
The sum of these divisors is 5136.
The arithmetic mean is 1284.

4 odd divisors

1, 7, 641, 4487

How to compute the divisors of 4487?

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 4487 by each of the numbers from 1 to 4487 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)

4487 / 1 = 4487 (the remainder is 0, so 1 is a divisor of 4487)
4487 / 2 = 2243.5 (the remainder is 1, so 2 is not a divisor of 4487)
4487 / 3 = 1495.6666666667 (the remainder is 2, so 3 is not a divisor of 4487)
...
4487 / 4486 = 1.0002229157379 (the remainder is 1, so 4486 is not a divisor of 4487)
4487 / 4487 = 1 (the remainder is 0, so 4487 is a divisor of 4487)

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 4487 (i.e. 66.985072964057). 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 $\frac{N}{d} = D$ )

4487 / 1 = 4487 (the remainder is 0, so 1 and 4487 are divisors of 4487)
4487 / 2 = 2243.5 (the remainder is 1, so 2 is not a divisor of 4487)
4487 / 3 = 1495.6666666667 (the remainder is 2, so 3 is not a divisor of 4487)
...
4487 / 65 = 69.030769230769 (the remainder is 2, so 65 is not a divisor of 4487)
4487 / 66 = 67.984848484848 (the remainder is 65, so 66 is not a divisor of 4487)