What are the divisors of 3779?

1, 3779

There is a total of 2 positive divisors.
The sum of these divisors is 3780.
The arithmetic mean is 1890.

2 odd divisors

1, 3779

How to compute the divisors of 3779?

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 3779 by each of the numbers from 1 to 3779 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)

3779 / 1 = 3779 (the remainder is 0, so 1 is a divisor of 3779)
3779 / 2 = 1889.5 (the remainder is 1, so 2 is not a divisor of 3779)
3779 / 3 = 1259.6666666667 (the remainder is 2, so 3 is not a divisor of 3779)
...
3779 / 3778 = 1.0002646903123 (the remainder is 1, so 3778 is not a divisor of 3779)
3779 / 3779 = 1 (the remainder is 0, so 3779 is a divisor of 3779)

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 3779 (i.e. 61.473571557215). 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 $\frac{N}{d} = D$ )

3779 / 1 = 3779 (the remainder is 0, so 1 and 3779 are divisors of 3779)
3779 / 2 = 1889.5 (the remainder is 1, so 2 is not a divisor of 3779)
3779 / 3 = 1259.6666666667 (the remainder is 2, so 3 is not a divisor of 3779)
...
3779 / 60 = 62.983333333333 (the remainder is 59, so 60 is not a divisor of 3779)
3779 / 61 = 61.950819672131 (the remainder is 58, so 61 is not a divisor of 3779)