What are the divisors of 4402?

1, 2, 31, 62, 71, 142, 2201, 4402

There is a total of 8 positive divisors.
The sum of these divisors is 6912.
The arithmetic mean is 864.

4 even divisors

2, 62, 142, 4402

4 odd divisors

1, 31, 71, 2201

How to compute the divisors of 4402?

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 4402 by each of the numbers from 1 to 4402 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)

4402 / 1 = 4402 (the remainder is 0, so 1 is a divisor of 4402)
4402 / 2 = 2201 (the remainder is 0, so 2 is a divisor of 4402)
4402 / 3 = 1467.3333333333 (the remainder is 1, so 3 is not a divisor of 4402)
...
4402 / 4401 = 1.0002272210861 (the remainder is 1, so 4401 is not a divisor of 4402)
4402 / 4402 = 1 (the remainder is 0, so 4402 is a divisor of 4402)

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 4402 (i.e. 66.347569661593). 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 $\frac{N}{d} = D$ )

4402 / 1 = 4402 (the remainder is 0, so 1 and 4402 are divisors of 4402)
4402 / 2 = 2201 (the remainder is 0, so 2 and 2201 are divisors of 4402)
4402 / 3 = 1467.3333333333 (the remainder is 1, so 3 is not a divisor of 4402)
...
4402 / 65 = 67.723076923077 (the remainder is 47, so 65 is not a divisor of 4402)
4402 / 66 = 66.69696969697 (the remainder is 46, so 66 is not a divisor of 4402)