What are the divisors of 4403?

1, 7, 17, 37, 119, 259, 629, 4403

There is a total of 8 positive divisors.
The sum of these divisors is 5472.
The arithmetic mean is 684.

8 odd divisors

1, 7, 17, 37, 119, 259, 629, 4403

How to compute the divisors of 4403?

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 4403 by each of the numbers from 1 to 4403 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)

4403 / 1 = 4403 (the remainder is 0, so 1 is a divisor of 4403)
4403 / 2 = 2201.5 (the remainder is 1, so 2 is not a divisor of 4403)
4403 / 3 = 1467.6666666667 (the remainder is 2, so 3 is not a divisor of 4403)
...
4403 / 4402 = 1.0002271694684 (the remainder is 1, so 4402 is not a divisor of 4403)
4403 / 4403 = 1 (the remainder is 0, so 4403 is a divisor of 4403)

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 4403 (i.e. 66.355105304716). 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 $\frac{N}{d} = D$ )

4403 / 1 = 4403 (the remainder is 0, so 1 and 4403 are divisors of 4403)
4403 / 2 = 2201.5 (the remainder is 1, so 2 is not a divisor of 4403)
4403 / 3 = 1467.6666666667 (the remainder is 2, so 3 is not a divisor of 4403)
...
4403 / 65 = 67.738461538462 (the remainder is 48, so 65 is not a divisor of 4403)
4403 / 66 = 66.712121212121 (the remainder is 47, so 66 is not a divisor of 4403)