What are the divisors of 1282?

1, 2, 641, 1282

There is a total of 4 positive divisors.
The sum of these divisors is 1926.
The arithmetic mean is 481.5.

2 even divisors

2, 1282

2 odd divisors

1, 641

How to compute the divisors of 1282?

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 1282 by each of the numbers from 1 to 1282 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)

1282 / 1 = 1282 (the remainder is 0, so 1 is a divisor of 1282)
1282 / 2 = 641 (the remainder is 0, so 2 is a divisor of 1282)
1282 / 3 = 427.33333333333 (the remainder is 1, so 3 is not a divisor of 1282)
...
1282 / 1281 = 1.0007806401249 (the remainder is 1, so 1281 is not a divisor of 1282)
1282 / 1282 = 1 (the remainder is 0, so 1282 is a divisor of 1282)

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 1282 (i.e. 35.805027579936). 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 $\frac{N}{d} = D$ )

1282 / 1 = 1282 (the remainder is 0, so 1 and 1282 are divisors of 1282)
1282 / 2 = 641 (the remainder is 0, so 2 and 641 are divisors of 1282)
1282 / 3 = 427.33333333333 (the remainder is 1, so 3 is not a divisor of 1282)
...
1282 / 34 = 37.705882352941 (the remainder is 24, so 34 is not a divisor of 1282)
1282 / 35 = 36.628571428571 (the remainder is 22, so 35 is not a divisor of 1282)