What are the divisors of 3719?

1, 3719

There is a total of 2 positive divisors.
The sum of these divisors is 3720.
The arithmetic mean is 1860.

2 odd divisors

1, 3719

How to compute the divisors of 3719?

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 3719 by each of the numbers from 1 to 3719 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)

3719 / 1 = 3719 (the remainder is 0, so 1 is a divisor of 3719)
3719 / 2 = 1859.5 (the remainder is 1, so 2 is not a divisor of 3719)
3719 / 3 = 1239.6666666667 (the remainder is 2, so 3 is not a divisor of 3719)
...
3719 / 3718 = 1.0002689618074 (the remainder is 1, so 3718 is not a divisor of 3719)
3719 / 3719 = 1 (the remainder is 0, so 3719 is a divisor of 3719)

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 3719 (i.e. 60.983604353957). 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 $\frac{N}{d} = D$ )

3719 / 1 = 3719 (the remainder is 0, so 1 and 3719 are divisors of 3719)
3719 / 2 = 1859.5 (the remainder is 1, so 2 is not a divisor of 3719)
3719 / 3 = 1239.6666666667 (the remainder is 2, so 3 is not a divisor of 3719)
...
3719 / 59 = 63.033898305085 (the remainder is 2, so 59 is not a divisor of 3719)
3719 / 60 = 61.983333333333 (the remainder is 59, so 60 is not a divisor of 3719)