What are the divisors of 4415?

1, 5, 883, 4415

There is a total of 4 positive divisors.
The sum of these divisors is 5304.
The arithmetic mean is 1326.

4 odd divisors

1, 5, 883, 4415

How to compute the divisors of 4415?

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 4415 by each of the numbers from 1 to 4415 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)

4415 / 1 = 4415 (the remainder is 0, so 1 is a divisor of 4415)
4415 / 2 = 2207.5 (the remainder is 1, so 2 is not a divisor of 4415)
4415 / 3 = 1471.6666666667 (the remainder is 2, so 3 is not a divisor of 4415)
...
4415 / 4414 = 1.0002265518804 (the remainder is 1, so 4414 is not a divisor of 4415)
4415 / 4415 = 1 (the remainder is 0, so 4415 is a divisor of 4415)

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 4415 (i.e. 66.445466361521). 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 $\frac{N}{d} = D$ )

4415 / 1 = 4415 (the remainder is 0, so 1 and 4415 are divisors of 4415)
4415 / 2 = 2207.5 (the remainder is 1, so 2 is not a divisor of 4415)
4415 / 3 = 1471.6666666667 (the remainder is 2, so 3 is not a divisor of 4415)
...
4415 / 65 = 67.923076923077 (the remainder is 60, so 65 is not a divisor of 4415)
4415 / 66 = 66.893939393939 (the remainder is 59, so 66 is not a divisor of 4415)