What are the divisors of 1175?

1, 5, 25, 47, 235, 1175

There is a total of 6 positive divisors.
The sum of these divisors is 1488.
The arithmetic mean is 248.

6 odd divisors

1, 5, 25, 47, 235, 1175

How to compute the divisors of 1175?

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 1175 by each of the numbers from 1 to 1175 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)

1175 / 1 = 1175 (the remainder is 0, so 1 is a divisor of 1175)
1175 / 2 = 587.5 (the remainder is 1, so 2 is not a divisor of 1175)
1175 / 3 = 391.66666666667 (the remainder is 2, so 3 is not a divisor of 1175)
...
1175 / 1174 = 1.0008517887564 (the remainder is 1, so 1174 is not a divisor of 1175)
1175 / 1175 = 1 (the remainder is 0, so 1175 is a divisor of 1175)

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 1175 (i.e. 34.278273002005). 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 $\frac{N}{d} = D$ )

1175 / 1 = 1175 (the remainder is 0, so 1 and 1175 are divisors of 1175)
1175 / 2 = 587.5 (the remainder is 1, so 2 is not a divisor of 1175)
1175 / 3 = 391.66666666667 (the remainder is 2, so 3 is not a divisor of 1175)
...
1175 / 33 = 35.606060606061 (the remainder is 20, so 33 is not a divisor of 1175)
1175 / 34 = 34.558823529412 (the remainder is 19, so 34 is not a divisor of 1175)