What are the divisors of 1190?

1, 2, 5, 7, 10, 14, 17, 34, 35, 70, 85, 119, 170, 238, 595, 1190

There is a total of 16 positive divisors.
The sum of these divisors is 2592.
The arithmetic mean is 162.

8 even divisors

2, 10, 14, 34, 70, 170, 238, 1190

8 odd divisors

1, 5, 7, 17, 35, 85, 119, 595

How to compute the divisors of 1190?

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 1190 by each of the numbers from 1 to 1190 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)

1190 / 1 = 1190 (the remainder is 0, so 1 is a divisor of 1190)
1190 / 2 = 595 (the remainder is 0, so 2 is a divisor of 1190)
1190 / 3 = 396.66666666667 (the remainder is 2, so 3 is not a divisor of 1190)
...
1190 / 1189 = 1.0008410428932 (the remainder is 1, so 1189 is not a divisor of 1190)
1190 / 1190 = 1 (the remainder is 0, so 1190 is a divisor of 1190)

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 1190 (i.e. 34.496376621321). 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 $\frac{N}{d} = D$ )

1190 / 1 = 1190 (the remainder is 0, so 1 and 1190 are divisors of 1190)
1190 / 2 = 595 (the remainder is 0, so 2 and 595 are divisors of 1190)
1190 / 3 = 396.66666666667 (the remainder is 2, so 3 is not a divisor of 1190)
...
1190 / 33 = 36.060606060606 (the remainder is 2, so 33 is not a divisor of 1190)
1190 / 34 = 35 (the remainder is 0, so 34 and 35 are divisors of 1190)