What are the divisors of 1192?

1, 2, 4, 8, 149, 298, 596, 1192

There is a total of 8 positive divisors.
The sum of these divisors is 2250.
The arithmetic mean is 281.25.

6 even divisors

2, 4, 8, 298, 596, 1192

2 odd divisors

1, 149

How to compute the divisors of 1192?

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 1192 by each of the numbers from 1 to 1192 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)

1192 / 1 = 1192 (the remainder is 0, so 1 is a divisor of 1192)
1192 / 2 = 596 (the remainder is 0, so 2 is a divisor of 1192)
1192 / 3 = 397.33333333333 (the remainder is 1, so 3 is not a divisor of 1192)
...
1192 / 1191 = 1.0008396305626 (the remainder is 1, so 1191 is not a divisor of 1192)
1192 / 1192 = 1 (the remainder is 0, so 1192 is a divisor of 1192)

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 1192 (i.e. 34.525353003264). 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 $\frac{N}{d} = D$ )

1192 / 1 = 1192 (the remainder is 0, so 1 and 1192 are divisors of 1192)
1192 / 2 = 596 (the remainder is 0, so 2 and 596 are divisors of 1192)
1192 / 3 = 397.33333333333 (the remainder is 1, so 3 is not a divisor of 1192)
...
1192 / 33 = 36.121212121212 (the remainder is 4, so 33 is not a divisor of 1192)
1192 / 34 = 35.058823529412 (the remainder is 2, so 34 is not a divisor of 1192)