What are the divisors of 949?

1, 13, 73, 949

There is a total of 4 positive divisors.
The sum of these divisors is 1036.
The arithmetic mean is 259.

4 odd divisors

1, 13, 73, 949

How to compute the divisors of 949?

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 949 by each of the numbers from 1 to 949 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)

949 / 1 = 949 (the remainder is 0, so 1 is a divisor of 949)
949 / 2 = 474.5 (the remainder is 1, so 2 is not a divisor of 949)
949 / 3 = 316.33333333333 (the remainder is 1, so 3 is not a divisor of 949)
...
949 / 948 = 1.0010548523207 (the remainder is 1, so 948 is not a divisor of 949)
949 / 949 = 1 (the remainder is 0, so 949 is a divisor of 949)

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 949 (i.e. 30.805843601499). 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 $\frac{N}{d} = D$ )

949 / 1 = 949 (the remainder is 0, so 1 and 949 are divisors of 949)
949 / 2 = 474.5 (the remainder is 1, so 2 is not a divisor of 949)
949 / 3 = 316.33333333333 (the remainder is 1, so 3 is not a divisor of 949)
...
949 / 29 = 32.724137931034 (the remainder is 21, so 29 is not a divisor of 949)
949 / 30 = 31.633333333333 (the remainder is 19, so 30 is not a divisor of 949)