What are the divisors of 3921?

1, 3, 1307, 3921

There is a total of 4 positive divisors.
The sum of these divisors is 5232.
The arithmetic mean is 1308.

4 odd divisors

1, 3, 1307, 3921

How to compute the divisors of 3921?

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 3921 by each of the numbers from 1 to 3921 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)

3921 / 1 = 3921 (the remainder is 0, so 1 is a divisor of 3921)
3921 / 2 = 1960.5 (the remainder is 1, so 2 is not a divisor of 3921)
3921 / 3 = 1307 (the remainder is 0, so 3 is a divisor of 3921)
...
3921 / 3920 = 1.0002551020408 (the remainder is 1, so 3920 is not a divisor of 3921)
3921 / 3921 = 1 (the remainder is 0, so 3921 is a divisor of 3921)

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 3921 (i.e. 62.617888817813). 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 $\frac{N}{d} = D$ )

3921 / 1 = 3921 (the remainder is 0, so 1 and 3921 are divisors of 3921)
3921 / 2 = 1960.5 (the remainder is 1, so 2 is not a divisor of 3921)
3921 / 3 = 1307 (the remainder is 0, so 3 and 1307 are divisors of 3921)
...
3921 / 61 = 64.27868852459 (the remainder is 17, so 61 is not a divisor of 3921)
3921 / 62 = 63.241935483871 (the remainder is 15, so 62 is not a divisor of 3921)