What are the divisors of 3778?

1, 2, 1889, 3778

There is a total of 4 positive divisors.
The sum of these divisors is 5670.
The arithmetic mean is 1417.5.

2 even divisors

2, 3778

2 odd divisors

1, 1889

How to compute the divisors of 3778?

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 3778 by each of the numbers from 1 to 3778 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)

3778 / 1 = 3778 (the remainder is 0, so 1 is a divisor of 3778)
3778 / 2 = 1889 (the remainder is 0, so 2 is a divisor of 3778)
3778 / 3 = 1259.3333333333 (the remainder is 1, so 3 is not a divisor of 3778)
...
3778 / 3777 = 1.0002647603918 (the remainder is 1, so 3777 is not a divisor of 3778)
3778 / 3778 = 1 (the remainder is 0, so 3778 is a divisor of 3778)

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 3778 (i.e. 61.465437442517). 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 $\frac{N}{d} = D$ )

3778 / 1 = 3778 (the remainder is 0, so 1 and 3778 are divisors of 3778)
3778 / 2 = 1889 (the remainder is 0, so 2 and 1889 are divisors of 3778)
3778 / 3 = 1259.3333333333 (the remainder is 1, so 3 is not a divisor of 3778)
...
3778 / 60 = 62.966666666667 (the remainder is 58, so 60 is not a divisor of 3778)
3778 / 61 = 61.934426229508 (the remainder is 57, so 61 is not a divisor of 3778)