What are the divisors of 244?

1, 2, 4, 61, 122, 244

There is a total of 6 positive divisors.
The sum of these divisors is 434.
The arithmetic mean is 72.333333333333.

4 even divisors

2, 4, 122, 244

2 odd divisors

1, 61

How to compute the divisors of 244?

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 244 by each of the numbers from 1 to 244 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)

244 / 1 = 244 (the remainder is 0, so 1 is a divisor of 244)
244 / 2 = 122 (the remainder is 0, so 2 is a divisor of 244)
244 / 3 = 81.333333333333 (the remainder is 1, so 3 is not a divisor of 244)
...
244 / 243 = 1.0041152263374 (the remainder is 1, so 243 is not a divisor of 244)
244 / 244 = 1 (the remainder is 0, so 244 is a divisor of 244)

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 244 (i.e. 15.620499351813). 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 $\frac{N}{d} = D$ )

244 / 1 = 244 (the remainder is 0, so 1 and 244 are divisors of 244)
244 / 2 = 122 (the remainder is 0, so 2 and 122 are divisors of 244)
244 / 3 = 81.333333333333 (the remainder is 1, so 3 is not a divisor of 244)
...
244 / 14 = 17.428571428571 (the remainder is 6, so 14 is not a divisor of 244)
244 / 15 = 16.266666666667 (the remainder is 4, so 15 is not a divisor of 244)