What are the divisors of 1294?

1, 2, 647, 1294

There is a total of 4 positive divisors.
The sum of these divisors is 1944.
The arithmetic mean is 486.

2 even divisors

2, 1294

2 odd divisors

1, 647

How to compute the divisors of 1294?

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 1294 by each of the numbers from 1 to 1294 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)

1294 / 1 = 1294 (the remainder is 0, so 1 is a divisor of 1294)
1294 / 2 = 647 (the remainder is 0, so 2 is a divisor of 1294)
1294 / 3 = 431.33333333333 (the remainder is 1, so 3 is not a divisor of 1294)
...
1294 / 1293 = 1.0007733952049 (the remainder is 1, so 1293 is not a divisor of 1294)
1294 / 1294 = 1 (the remainder is 0, so 1294 is a divisor of 1294)

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 1294 (i.e. 35.97221149721). 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 $\frac{N}{d} = D$ )

1294 / 1 = 1294 (the remainder is 0, so 1 and 1294 are divisors of 1294)
1294 / 2 = 647 (the remainder is 0, so 2 and 647 are divisors of 1294)
1294 / 3 = 431.33333333333 (the remainder is 1, so 3 is not a divisor of 1294)
...
1294 / 34 = 38.058823529412 (the remainder is 2, so 34 is not a divisor of 1294)
1294 / 35 = 36.971428571429 (the remainder is 34, so 35 is not a divisor of 1294)