What are the divisors of 3949?

1, 11, 359, 3949

There is a total of 4 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 1080.

4 odd divisors

1, 11, 359, 3949

How to compute the divisors of 3949?

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 3949 by each of the numbers from 1 to 3949 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)

3949 / 1 = 3949 (the remainder is 0, so 1 is a divisor of 3949)
3949 / 2 = 1974.5 (the remainder is 1, so 2 is not a divisor of 3949)
3949 / 3 = 1316.3333333333 (the remainder is 1, so 3 is not a divisor of 3949)
...
3949 / 3948 = 1.0002532928065 (the remainder is 1, so 3948 is not a divisor of 3949)
3949 / 3949 = 1 (the remainder is 0, so 3949 is a divisor of 3949)

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 3949 (i.e. 62.84106937346). 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 $\frac{N}{d} = D$ )

3949 / 1 = 3949 (the remainder is 0, so 1 and 3949 are divisors of 3949)
3949 / 2 = 1974.5 (the remainder is 1, so 2 is not a divisor of 3949)
3949 / 3 = 1316.3333333333 (the remainder is 1, so 3 is not a divisor of 3949)
...
3949 / 61 = 64.737704918033 (the remainder is 45, so 61 is not a divisor of 3949)
3949 / 62 = 63.693548387097 (the remainder is 43, so 62 is not a divisor of 3949)