What are the divisors of 4450?

1, 2, 5, 10, 25, 50, 89, 178, 445, 890, 2225, 4450

There is a total of 12 positive divisors.
The sum of these divisors is 8370.
The arithmetic mean is 697.5.

6 even divisors

2, 10, 50, 178, 890, 4450

6 odd divisors

1, 5, 25, 89, 445, 2225

How to compute the divisors of 4450?

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 4450 by each of the numbers from 1 to 4450 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)

4450 / 1 = 4450 (the remainder is 0, so 1 is a divisor of 4450)
4450 / 2 = 2225 (the remainder is 0, so 2 is a divisor of 4450)
4450 / 3 = 1483.3333333333 (the remainder is 1, so 3 is not a divisor of 4450)
...
4450 / 4449 = 1.0002247696111 (the remainder is 1, so 4449 is not a divisor of 4450)
4450 / 4450 = 1 (the remainder is 0, so 4450 is a divisor of 4450)

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 4450 (i.e. 66.708320320632). 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 $\frac{N}{d} = D$ )

4450 / 1 = 4450 (the remainder is 0, so 1 and 4450 are divisors of 4450)
4450 / 2 = 2225 (the remainder is 0, so 2 and 2225 are divisors of 4450)
4450 / 3 = 1483.3333333333 (the remainder is 1, so 3 is not a divisor of 4450)
...
4450 / 65 = 68.461538461538 (the remainder is 30, so 65 is not a divisor of 4450)
4450 / 66 = 67.424242424242 (the remainder is 28, so 66 is not a divisor of 4450)