What are the divisors of 3953?

1, 59, 67, 3953

There is a total of 4 positive divisors.
The sum of these divisors is 4080.
The arithmetic mean is 1020.

4 odd divisors

1, 59, 67, 3953

How to compute the divisors of 3953?

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 3953 by each of the numbers from 1 to 3953 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)

3953 / 1 = 3953 (the remainder is 0, so 1 is a divisor of 3953)
3953 / 2 = 1976.5 (the remainder is 1, so 2 is not a divisor of 3953)
3953 / 3 = 1317.6666666667 (the remainder is 2, so 3 is not a divisor of 3953)
...
3953 / 3952 = 1.0002530364372 (the remainder is 1, so 3952 is not a divisor of 3953)
3953 / 3953 = 1 (the remainder is 0, so 3953 is a divisor of 3953)

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 3953 (i.e. 62.872887638473). 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 $\frac{N}{d} = D$ )

3953 / 1 = 3953 (the remainder is 0, so 1 and 3953 are divisors of 3953)
3953 / 2 = 1976.5 (the remainder is 1, so 2 is not a divisor of 3953)
3953 / 3 = 1317.6666666667 (the remainder is 2, so 3 is not a divisor of 3953)
...
3953 / 61 = 64.803278688525 (the remainder is 49, so 61 is not a divisor of 3953)
3953 / 62 = 63.758064516129 (the remainder is 47, so 62 is not a divisor of 3953)