What are the divisors of 1169?

1, 7, 167, 1169

There is a total of 4 positive divisors.
The sum of these divisors is 1344.
The arithmetic mean is 336.

4 odd divisors

1, 7, 167, 1169

How to compute the divisors of 1169?

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 1169 by each of the numbers from 1 to 1169 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)

1169 / 1 = 1169 (the remainder is 0, so 1 is a divisor of 1169)
1169 / 2 = 584.5 (the remainder is 1, so 2 is not a divisor of 1169)
1169 / 3 = 389.66666666667 (the remainder is 2, so 3 is not a divisor of 1169)
...
1169 / 1168 = 1.0008561643836 (the remainder is 1, so 1168 is not a divisor of 1169)
1169 / 1169 = 1 (the remainder is 0, so 1169 is a divisor of 1169)

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 1169 (i.e. 34.190641994558). 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 $\frac{N}{d} = D$ )

1169 / 1 = 1169 (the remainder is 0, so 1 and 1169 are divisors of 1169)
1169 / 2 = 584.5 (the remainder is 1, so 2 is not a divisor of 1169)
1169 / 3 = 389.66666666667 (the remainder is 2, so 3 is not a divisor of 1169)
...
1169 / 33 = 35.424242424242 (the remainder is 14, so 33 is not a divisor of 1169)
1169 / 34 = 34.382352941176 (the remainder is 13, so 34 is not a divisor of 1169)