What are the divisors of 3738?

1, 2, 3, 6, 7, 14, 21, 42, 89, 178, 267, 534, 623, 1246, 1869, 3738

There is a total of 16 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 540.

8 even divisors

2, 6, 14, 42, 178, 534, 1246, 3738

8 odd divisors

1, 3, 7, 21, 89, 267, 623, 1869

How to compute the divisors of 3738?

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 3738 by each of the numbers from 1 to 3738 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)

3738 / 1 = 3738 (the remainder is 0, so 1 is a divisor of 3738)
3738 / 2 = 1869 (the remainder is 0, so 2 is a divisor of 3738)
3738 / 3 = 1246 (the remainder is 0, so 3 is a divisor of 3738)
...
3738 / 3737 = 1.000267594327 (the remainder is 1, so 3737 is not a divisor of 3738)
3738 / 3738 = 1 (the remainder is 0, so 3738 is a divisor of 3738)

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 3738 (i.e. 61.139185470531). 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 $\frac{N}{d} = D$ )

3738 / 1 = 3738 (the remainder is 0, so 1 and 3738 are divisors of 3738)
3738 / 2 = 1869 (the remainder is 0, so 2 and 1869 are divisors of 3738)
3738 / 3 = 1246 (the remainder is 0, so 3 and 1246 are divisors of 3738)
...
3738 / 60 = 62.3 (the remainder is 18, so 60 is not a divisor of 3738)
3738 / 61 = 61.27868852459 (the remainder is 17, so 61 is not a divisor of 3738)