What are the divisors of 4412?

1, 2, 4, 1103, 2206, 4412

There is a total of 6 positive divisors.
The sum of these divisors is 7728.
The arithmetic mean is 1288.

4 even divisors

2, 4, 2206, 4412

2 odd divisors

1, 1103

How to compute the divisors of 4412?

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 4412 by each of the numbers from 1 to 4412 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)

4412 / 1 = 4412 (the remainder is 0, so 1 is a divisor of 4412)
4412 / 2 = 2206 (the remainder is 0, so 2 is a divisor of 4412)
4412 / 3 = 1470.6666666667 (the remainder is 2, so 3 is not a divisor of 4412)
...
4412 / 4411 = 1.0002267059624 (the remainder is 1, so 4411 is not a divisor of 4412)
4412 / 4412 = 1 (the remainder is 0, so 4412 is a divisor of 4412)

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 4412 (i.e. 66.422887621662). 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 $\frac{N}{d} = D$ )

4412 / 1 = 4412 (the remainder is 0, so 1 and 4412 are divisors of 4412)
4412 / 2 = 2206 (the remainder is 0, so 2 and 2206 are divisors of 4412)
4412 / 3 = 1470.6666666667 (the remainder is 2, so 3 is not a divisor of 4412)
...
4412 / 65 = 67.876923076923 (the remainder is 57, so 65 is not a divisor of 4412)
4412 / 66 = 66.848484848485 (the remainder is 56, so 66 is not a divisor of 4412)