What are the divisors of 4387?

1, 41, 107, 4387

There is a total of 4 positive divisors.
The sum of these divisors is 4536.
The arithmetic mean is 1134.

4 odd divisors

1, 41, 107, 4387

How to compute the divisors of 4387?

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 4387 by each of the numbers from 1 to 4387 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)

4387 / 1 = 4387 (the remainder is 0, so 1 is a divisor of 4387)
4387 / 2 = 2193.5 (the remainder is 1, so 2 is not a divisor of 4387)
4387 / 3 = 1462.3333333333 (the remainder is 1, so 3 is not a divisor of 4387)
...
4387 / 4386 = 1.000227998176 (the remainder is 1, so 4386 is not a divisor of 4387)
4387 / 4387 = 1 (the remainder is 0, so 4387 is a divisor of 4387)

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 4387 (i.e. 66.234432133144). 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 $\frac{N}{d} = D$ )

4387 / 1 = 4387 (the remainder is 0, so 1 and 4387 are divisors of 4387)
4387 / 2 = 2193.5 (the remainder is 1, so 2 is not a divisor of 4387)
4387 / 3 = 1462.3333333333 (the remainder is 1, so 3 is not a divisor of 4387)
...
4387 / 65 = 67.492307692308 (the remainder is 32, so 65 is not a divisor of 4387)
4387 / 66 = 66.469696969697 (the remainder is 31, so 66 is not a divisor of 4387)