What are the divisors of 1268?

1, 2, 4, 317, 634, 1268

There is a total of 6 positive divisors.
The sum of these divisors is 2226.
The arithmetic mean is 371.

4 even divisors

2, 4, 634, 1268

2 odd divisors

1, 317

How to compute the divisors of 1268?

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 1268 by each of the numbers from 1 to 1268 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)

1268 / 1 = 1268 (the remainder is 0, so 1 is a divisor of 1268)
1268 / 2 = 634 (the remainder is 0, so 2 is a divisor of 1268)
1268 / 3 = 422.66666666667 (the remainder is 2, so 3 is not a divisor of 1268)
...
1268 / 1267 = 1.0007892659826 (the remainder is 1, so 1267 is not a divisor of 1268)
1268 / 1268 = 1 (the remainder is 0, so 1268 is a divisor of 1268)

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 1268 (i.e. 35.60898762953). 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 $\frac{N}{d} = D$ )

1268 / 1 = 1268 (the remainder is 0, so 1 and 1268 are divisors of 1268)
1268 / 2 = 634 (the remainder is 0, so 2 and 634 are divisors of 1268)
1268 / 3 = 422.66666666667 (the remainder is 2, so 3 is not a divisor of 1268)
...
1268 / 34 = 37.294117647059 (the remainder is 10, so 34 is not a divisor of 1268)
1268 / 35 = 36.228571428571 (the remainder is 8, so 35 is not a divisor of 1268)