What are the divisors of 3769?

1, 3769

There is a total of 2 positive divisors.
The sum of these divisors is 3770.
The arithmetic mean is 1885.

2 odd divisors

1, 3769

How to compute the divisors of 3769?

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 3769 by each of the numbers from 1 to 3769 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)

3769 / 1 = 3769 (the remainder is 0, so 1 is a divisor of 3769)
3769 / 2 = 1884.5 (the remainder is 1, so 2 is not a divisor of 3769)
3769 / 3 = 1256.3333333333 (the remainder is 1, so 3 is not a divisor of 3769)
...
3769 / 3768 = 1.0002653927813 (the remainder is 1, so 3768 is not a divisor of 3769)
3769 / 3769 = 1 (the remainder is 0, so 3769 is a divisor of 3769)

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 3769 (i.e. 61.392181912683). 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 $\frac{N}{d} = D$ )

3769 / 1 = 3769 (the remainder is 0, so 1 and 3769 are divisors of 3769)
3769 / 2 = 1884.5 (the remainder is 1, so 2 is not a divisor of 3769)
3769 / 3 = 1256.3333333333 (the remainder is 1, so 3 is not a divisor of 3769)
...
3769 / 60 = 62.816666666667 (the remainder is 49, so 60 is not a divisor of 3769)
3769 / 61 = 61.786885245902 (the remainder is 48, so 61 is not a divisor of 3769)