What are the divisors of 1094?

1, 2, 547, 1094

There is a total of 4 positive divisors.
The sum of these divisors is 1644.
The arithmetic mean is 411.

2 even divisors

2, 1094

2 odd divisors

1, 547

How to compute the divisors of 1094?

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 1094 by each of the numbers from 1 to 1094 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)

1094 / 1 = 1094 (the remainder is 0, so 1 is a divisor of 1094)
1094 / 2 = 547 (the remainder is 0, so 2 is a divisor of 1094)
1094 / 3 = 364.66666666667 (the remainder is 2, so 3 is not a divisor of 1094)
...
1094 / 1093 = 1.0009149130833 (the remainder is 1, so 1093 is not a divisor of 1094)
1094 / 1094 = 1 (the remainder is 0, so 1094 is a divisor of 1094)

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 1094 (i.e. 33.075670817082). 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 $\frac{N}{d} = D$ )

1094 / 1 = 1094 (the remainder is 0, so 1 and 1094 are divisors of 1094)
1094 / 2 = 547 (the remainder is 0, so 2 and 547 are divisors of 1094)
1094 / 3 = 364.66666666667 (the remainder is 2, so 3 is not a divisor of 1094)
...
1094 / 32 = 34.1875 (the remainder is 6, so 32 is not a divisor of 1094)
1094 / 33 = 33.151515151515 (the remainder is 5, so 33 is not a divisor of 1094)