What are the divisors of 1256?

1, 2, 4, 8, 157, 314, 628, 1256

There is a total of 8 positive divisors.
The sum of these divisors is 2370.
The arithmetic mean is 296.25.

6 even divisors

2, 4, 8, 314, 628, 1256

2 odd divisors

1, 157

How to compute the divisors of 1256?

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 1256 by each of the numbers from 1 to 1256 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)

1256 / 1 = 1256 (the remainder is 0, so 1 is a divisor of 1256)
1256 / 2 = 628 (the remainder is 0, so 2 is a divisor of 1256)
1256 / 3 = 418.66666666667 (the remainder is 2, so 3 is not a divisor of 1256)
...
1256 / 1255 = 1.000796812749 (the remainder is 1, so 1255 is not a divisor of 1256)
1256 / 1256 = 1 (the remainder is 0, so 1256 is a divisor of 1256)

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 1256 (i.e. 35.440090293339). 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 $\frac{N}{d} = D$ )

1256 / 1 = 1256 (the remainder is 0, so 1 and 1256 are divisors of 1256)
1256 / 2 = 628 (the remainder is 0, so 2 and 628 are divisors of 1256)
1256 / 3 = 418.66666666667 (the remainder is 2, so 3 is not a divisor of 1256)
...
1256 / 34 = 36.941176470588 (the remainder is 32, so 34 is not a divisor of 1256)
1256 / 35 = 35.885714285714 (the remainder is 31, so 35 is not a divisor of 1256)