What are the divisors of 3877?

1, 3877

There is a total of 2 positive divisors.
The sum of these divisors is 3878.
The arithmetic mean is 1939.

2 odd divisors

1, 3877

How to compute the divisors of 3877?

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 3877 by each of the numbers from 1 to 3877 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)

3877 / 1 = 3877 (the remainder is 0, so 1 is a divisor of 3877)
3877 / 2 = 1938.5 (the remainder is 1, so 2 is not a divisor of 3877)
3877 / 3 = 1292.3333333333 (the remainder is 1, so 3 is not a divisor of 3877)
...
3877 / 3876 = 1.000257997936 (the remainder is 1, so 3876 is not a divisor of 3877)
3877 / 3877 = 1 (the remainder is 0, so 3877 is a divisor of 3877)

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 3877 (i.e. 62.265560304232). 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 $\frac{N}{d} = D$ )

3877 / 1 = 3877 (the remainder is 0, so 1 and 3877 are divisors of 3877)
3877 / 2 = 1938.5 (the remainder is 1, so 2 is not a divisor of 3877)
3877 / 3 = 1292.3333333333 (the remainder is 1, so 3 is not a divisor of 3877)
...
3877 / 61 = 63.55737704918 (the remainder is 34, so 61 is not a divisor of 3877)
3877 / 62 = 62.532258064516 (the remainder is 33, so 62 is not a divisor of 3877)