What are the divisors of 4469?

1, 41, 109, 4469

There is a total of 4 positive divisors.
The sum of these divisors is 4620.
The arithmetic mean is 1155.

4 odd divisors

1, 41, 109, 4469

How to compute the divisors of 4469?

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 4469 by each of the numbers from 1 to 4469 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)

4469 / 1 = 4469 (the remainder is 0, so 1 is a divisor of 4469)
4469 / 2 = 2234.5 (the remainder is 1, so 2 is not a divisor of 4469)
4469 / 3 = 1489.6666666667 (the remainder is 2, so 3 is not a divisor of 4469)
...
4469 / 4468 = 1.0002238137869 (the remainder is 1, so 4468 is not a divisor of 4469)
4469 / 4469 = 1 (the remainder is 0, so 4469 is a divisor of 4469)

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 4469 (i.e. 66.850579653433). 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 $\frac{N}{d} = D$ )

4469 / 1 = 4469 (the remainder is 0, so 1 and 4469 are divisors of 4469)
4469 / 2 = 2234.5 (the remainder is 1, so 2 is not a divisor of 4469)
4469 / 3 = 1489.6666666667 (the remainder is 2, so 3 is not a divisor of 4469)
...
4469 / 65 = 68.753846153846 (the remainder is 49, so 65 is not a divisor of 4469)
4469 / 66 = 67.712121212121 (the remainder is 47, so 66 is not a divisor of 4469)