What are the divisors of 3758?

1, 2, 1879, 3758

There is a total of 4 positive divisors.
The sum of these divisors is 5640.
The arithmetic mean is 1410.

2 even divisors

2, 3758

2 odd divisors

1, 1879

How to compute the divisors of 3758?

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 3758 by each of the numbers from 1 to 3758 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)

3758 / 1 = 3758 (the remainder is 0, so 1 is a divisor of 3758)
3758 / 2 = 1879 (the remainder is 0, so 2 is a divisor of 3758)
3758 / 3 = 1252.6666666667 (the remainder is 2, so 3 is not a divisor of 3758)
...
3758 / 3757 = 1.0002661698163 (the remainder is 1, so 3757 is not a divisor of 3758)
3758 / 3758 = 1 (the remainder is 0, so 3758 is a divisor of 3758)

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 3758 (i.e. 61.302528495976). 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 $\frac{N}{d} = D$ )

3758 / 1 = 3758 (the remainder is 0, so 1 and 3758 are divisors of 3758)
3758 / 2 = 1879 (the remainder is 0, so 2 and 1879 are divisors of 3758)
3758 / 3 = 1252.6666666667 (the remainder is 2, so 3 is not a divisor of 3758)
...
3758 / 60 = 62.633333333333 (the remainder is 38, so 60 is not a divisor of 3758)
3758 / 61 = 61.606557377049 (the remainder is 37, so 61 is not a divisor of 3758)