What are the divisors of 1292?

1, 2, 4, 17, 19, 34, 38, 68, 76, 323, 646, 1292

There is a total of 12 positive divisors.
The sum of these divisors is 2520.
The arithmetic mean is 210.

8 even divisors

2, 4, 34, 38, 68, 76, 646, 1292

4 odd divisors

1, 17, 19, 323

How to compute the divisors of 1292?

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 1292 by each of the numbers from 1 to 1292 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)

1292 / 1 = 1292 (the remainder is 0, so 1 is a divisor of 1292)
1292 / 2 = 646 (the remainder is 0, so 2 is a divisor of 1292)
1292 / 3 = 430.66666666667 (the remainder is 2, so 3 is not a divisor of 1292)
...
1292 / 1291 = 1.0007745933385 (the remainder is 1, so 1291 is not a divisor of 1292)
1292 / 1292 = 1 (the remainder is 0, so 1292 is a divisor of 1292)

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 1292 (i.e. 35.944401511223). 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 $\frac{N}{d} = D$ )

1292 / 1 = 1292 (the remainder is 0, so 1 and 1292 are divisors of 1292)
1292 / 2 = 646 (the remainder is 0, so 2 and 646 are divisors of 1292)
1292 / 3 = 430.66666666667 (the remainder is 2, so 3 is not a divisor of 1292)
...
1292 / 34 = 38 (the remainder is 0, so 34 and 38 are divisors of 1292)
1292 / 35 = 36.914285714286 (the remainder is 32, so 35 is not a divisor of 1292)