What are the divisors of 1244?

1, 2, 4, 311, 622, 1244

There is a total of 6 positive divisors.
The sum of these divisors is 2184.
The arithmetic mean is 364.

4 even divisors

2, 4, 622, 1244

2 odd divisors

1, 311

How to compute the divisors of 1244?

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 1244 by each of the numbers from 1 to 1244 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)

1244 / 1 = 1244 (the remainder is 0, so 1 is a divisor of 1244)
1244 / 2 = 622 (the remainder is 0, so 2 is a divisor of 1244)
1244 / 3 = 414.66666666667 (the remainder is 2, so 3 is not a divisor of 1244)
...
1244 / 1243 = 1.0008045052293 (the remainder is 1, so 1243 is not a divisor of 1244)
1244 / 1244 = 1 (the remainder is 0, so 1244 is a divisor of 1244)

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 1244 (i.e. 35.270384177097). 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 $\frac{N}{d} = D$ )

1244 / 1 = 1244 (the remainder is 0, so 1 and 1244 are divisors of 1244)
1244 / 2 = 622 (the remainder is 0, so 2 and 622 are divisors of 1244)
1244 / 3 = 414.66666666667 (the remainder is 2, so 3 is not a divisor of 1244)
...
1244 / 34 = 36.588235294118 (the remainder is 20, so 34 is not a divisor of 1244)
1244 / 35 = 35.542857142857 (the remainder is 19, so 35 is not a divisor of 1244)