What are the divisors of 4437?

1, 3, 9, 17, 29, 51, 87, 153, 261, 493, 1479, 4437

There is a total of 12 positive divisors.
The sum of these divisors is 7020.
The arithmetic mean is 585.

12 odd divisors

1, 3, 9, 17, 29, 51, 87, 153, 261, 493, 1479, 4437

How to compute the divisors of 4437?

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 4437 by each of the numbers from 1 to 4437 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)

4437 / 1 = 4437 (the remainder is 0, so 1 is a divisor of 4437)
4437 / 2 = 2218.5 (the remainder is 1, so 2 is not a divisor of 4437)
4437 / 3 = 1479 (the remainder is 0, so 3 is a divisor of 4437)
...
4437 / 4436 = 1.0002254283138 (the remainder is 1, so 4436 is not a divisor of 4437)
4437 / 4437 = 1 (the remainder is 0, so 4437 is a divisor of 4437)

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 4437 (i.e. 66.610809933524). 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 $\frac{N}{d} = D$ )

4437 / 1 = 4437 (the remainder is 0, so 1 and 4437 are divisors of 4437)
4437 / 2 = 2218.5 (the remainder is 1, so 2 is not a divisor of 4437)
4437 / 3 = 1479 (the remainder is 0, so 3 and 1479 are divisors of 4437)
...
4437 / 65 = 68.261538461538 (the remainder is 17, so 65 is not a divisor of 4437)
4437 / 66 = 67.227272727273 (the remainder is 15, so 66 is not a divisor of 4437)