What are the divisors of 4244?

1, 2, 4, 1061, 2122, 4244

There is a total of 6 positive divisors.
The sum of these divisors is 7434.
The arithmetic mean is 1239.

4 even divisors

2, 4, 2122, 4244

2 odd divisors

1, 1061

How to compute the divisors of 4244?

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 4244 by each of the numbers from 1 to 4244 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)

4244 / 1 = 4244 (the remainder is 0, so 1 is a divisor of 4244)
4244 / 2 = 2122 (the remainder is 0, so 2 is a divisor of 4244)
4244 / 3 = 1414.6666666667 (the remainder is 2, so 3 is not a divisor of 4244)
...
4244 / 4243 = 1.0002356823003 (the remainder is 1, so 4243 is not a divisor of 4244)
4244 / 4244 = 1 (the remainder is 0, so 4244 is a divisor of 4244)

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 4244 (i.e. 65.145989899609). 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 $\frac{N}{d} = D$ )

4244 / 1 = 4244 (the remainder is 0, so 1 and 4244 are divisors of 4244)
4244 / 2 = 2122 (the remainder is 0, so 2 and 2122 are divisors of 4244)
4244 / 3 = 1414.6666666667 (the remainder is 2, so 3 is not a divisor of 4244)
...
4244 / 64 = 66.3125 (the remainder is 20, so 64 is not a divisor of 4244)
4244 / 65 = 65.292307692308 (the remainder is 19, so 65 is not a divisor of 4244)