What are the divisors of 3777?

1, 3, 1259, 3777

There is a total of 4 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 1260.

4 odd divisors

1, 3, 1259, 3777

How to compute the divisors of 3777?

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 3777 by each of the numbers from 1 to 3777 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)

3777 / 1 = 3777 (the remainder is 0, so 1 is a divisor of 3777)
3777 / 2 = 1888.5 (the remainder is 1, so 2 is not a divisor of 3777)
3777 / 3 = 1259 (the remainder is 0, so 3 is a divisor of 3777)
...
3777 / 3776 = 1.0002648305085 (the remainder is 1, so 3776 is not a divisor of 3777)
3777 / 3777 = 1 (the remainder is 0, so 3777 is a divisor of 3777)

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 3777 (i.e. 61.457302251238). 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 $\frac{N}{d} = D$ )

3777 / 1 = 3777 (the remainder is 0, so 1 and 3777 are divisors of 3777)
3777 / 2 = 1888.5 (the remainder is 1, so 2 is not a divisor of 3777)
3777 / 3 = 1259 (the remainder is 0, so 3 and 1259 are divisors of 3777)
...
3777 / 60 = 62.95 (the remainder is 57, so 60 is not a divisor of 3777)
3777 / 61 = 61.918032786885 (the remainder is 56, so 61 is not a divisor of 3777)