What are the divisors of 1194?

1, 2, 3, 6, 199, 398, 597, 1194

There is a total of 8 positive divisors.
The sum of these divisors is 2400.
The arithmetic mean is 300.

4 even divisors

2, 6, 398, 1194

4 odd divisors

1, 3, 199, 597

How to compute the divisors of 1194?

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 1194 by each of the numbers from 1 to 1194 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)

1194 / 1 = 1194 (the remainder is 0, so 1 is a divisor of 1194)
1194 / 2 = 597 (the remainder is 0, so 2 is a divisor of 1194)
1194 / 3 = 398 (the remainder is 0, so 3 is a divisor of 1194)
...
1194 / 1193 = 1.0008382229673 (the remainder is 1, so 1193 is not a divisor of 1194)
1194 / 1194 = 1 (the remainder is 0, so 1194 is a divisor of 1194)

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 1194 (i.e. 34.554305086342). 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 $\frac{N}{d} = D$ )

1194 / 1 = 1194 (the remainder is 0, so 1 and 1194 are divisors of 1194)
1194 / 2 = 597 (the remainder is 0, so 2 and 597 are divisors of 1194)
1194 / 3 = 398 (the remainder is 0, so 3 and 398 are divisors of 1194)
...
1194 / 33 = 36.181818181818 (the remainder is 6, so 33 is not a divisor of 1194)
1194 / 34 = 35.117647058824 (the remainder is 4, so 34 is not a divisor of 1194)