What are the divisors of 4454?

1, 2, 17, 34, 131, 262, 2227, 4454

There is a total of 8 positive divisors.
The sum of these divisors is 7128.
The arithmetic mean is 891.

4 even divisors

2, 34, 262, 4454

4 odd divisors

1, 17, 131, 2227

How to compute the divisors of 4454?

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 4454 by each of the numbers from 1 to 4454 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)

4454 / 1 = 4454 (the remainder is 0, so 1 is a divisor of 4454)
4454 / 2 = 2227 (the remainder is 0, so 2 is a divisor of 4454)
4454 / 3 = 1484.6666666667 (the remainder is 2, so 3 is not a divisor of 4454)
...
4454 / 4453 = 1.0002245677072 (the remainder is 1, so 4453 is not a divisor of 4454)
4454 / 4454 = 1 (the remainder is 0, so 4454 is a divisor of 4454)

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 4454 (i.e. 66.738294853854). 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 $\frac{N}{d} = D$ )

4454 / 1 = 4454 (the remainder is 0, so 1 and 4454 are divisors of 4454)
4454 / 2 = 2227 (the remainder is 0, so 2 and 2227 are divisors of 4454)
4454 / 3 = 1484.6666666667 (the remainder is 2, so 3 is not a divisor of 4454)
...
4454 / 65 = 68.523076923077 (the remainder is 34, so 65 is not a divisor of 4454)
4454 / 66 = 67.484848484848 (the remainder is 32, so 66 is not a divisor of 4454)