What are the divisors of 1078?

1, 2, 7, 11, 14, 22, 49, 77, 98, 154, 539, 1078

There is a total of 12 positive divisors.
The sum of these divisors is 2052.
The arithmetic mean is 171.

6 even divisors

2, 14, 22, 98, 154, 1078

6 odd divisors

1, 7, 11, 49, 77, 539

How to compute the divisors of 1078?

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 1078 by each of the numbers from 1 to 1078 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)

1078 / 1 = 1078 (the remainder is 0, so 1 is a divisor of 1078)
1078 / 2 = 539 (the remainder is 0, so 2 is a divisor of 1078)
1078 / 3 = 359.33333333333 (the remainder is 1, so 3 is not a divisor of 1078)
...
1078 / 1077 = 1.0009285051068 (the remainder is 1, so 1077 is not a divisor of 1078)
1078 / 1078 = 1 (the remainder is 0, so 1078 is a divisor of 1078)

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 1078 (i.e. 32.832910318764). 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 $\frac{N}{d} = D$ )

1078 / 1 = 1078 (the remainder is 0, so 1 and 1078 are divisors of 1078)
1078 / 2 = 539 (the remainder is 0, so 2 and 539 are divisors of 1078)
1078 / 3 = 359.33333333333 (the remainder is 1, so 3 is not a divisor of 1078)
...
1078 / 31 = 34.774193548387 (the remainder is 24, so 31 is not a divisor of 1078)
1078 / 32 = 33.6875 (the remainder is 22, so 32 is not a divisor of 1078)