What are the divisors of 3701?

1, 3701

There is a total of 2 positive divisors.
The sum of these divisors is 3702.
The arithmetic mean is 1851.

2 odd divisors

1, 3701

How to compute the divisors of 3701?

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 3701 by each of the numbers from 1 to 3701 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)

3701 / 1 = 3701 (the remainder is 0, so 1 is a divisor of 3701)
3701 / 2 = 1850.5 (the remainder is 1, so 2 is not a divisor of 3701)
3701 / 3 = 1233.6666666667 (the remainder is 2, so 3 is not a divisor of 3701)
...
3701 / 3700 = 1.0002702702703 (the remainder is 1, so 3700 is not a divisor of 3701)
3701 / 3701 = 1 (the remainder is 0, so 3701 is a divisor of 3701)

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 3701 (i.e. 60.835844697021). 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 $\frac{N}{d} = D$ )

3701 / 1 = 3701 (the remainder is 0, so 1 and 3701 are divisors of 3701)
3701 / 2 = 1850.5 (the remainder is 1, so 2 is not a divisor of 3701)
3701 / 3 = 1233.6666666667 (the remainder is 2, so 3 is not a divisor of 3701)
...
3701 / 59 = 62.728813559322 (the remainder is 43, so 59 is not a divisor of 3701)
3701 / 60 = 61.683333333333 (the remainder is 41, so 60 is not a divisor of 3701)