What are the divisors of 4474?

1, 2, 2237, 4474

There is a total of 4 positive divisors.
The sum of these divisors is 6714.
The arithmetic mean is 1678.5.

2 even divisors

2, 4474

2 odd divisors

1, 2237

How to compute the divisors of 4474?

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 4474 by each of the numbers from 1 to 4474 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)

4474 / 1 = 4474 (the remainder is 0, so 1 is a divisor of 4474)
4474 / 2 = 2237 (the remainder is 0, so 2 is a divisor of 4474)
4474 / 3 = 1491.3333333333 (the remainder is 1, so 3 is not a divisor of 4474)
...
4474 / 4473 = 1.0002235636038 (the remainder is 1, so 4473 is not a divisor of 4474)
4474 / 4474 = 1 (the remainder is 0, so 4474 is a divisor of 4474)

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 4474 (i.e. 66.887966032763). 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 $\frac{N}{d} = D$ )

4474 / 1 = 4474 (the remainder is 0, so 1 and 4474 are divisors of 4474)
4474 / 2 = 2237 (the remainder is 0, so 2 and 2237 are divisors of 4474)
4474 / 3 = 1491.3333333333 (the remainder is 1, so 3 is not a divisor of 4474)
...
4474 / 65 = 68.830769230769 (the remainder is 54, so 65 is not a divisor of 4474)
4474 / 66 = 67.787878787879 (the remainder is 52, so 66 is not a divisor of 4474)