What are the divisors of 3676?

1, 2, 4, 919, 1838, 3676

There is a total of 6 positive divisors.
The sum of these divisors is 6440.
The arithmetic mean is 1073.3333333333.

4 even divisors

2, 4, 1838, 3676

2 odd divisors

1, 919

How to compute the divisors of 3676?

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 3676 by each of the numbers from 1 to 3676 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)

3676 / 1 = 3676 (the remainder is 0, so 1 is a divisor of 3676)
3676 / 2 = 1838 (the remainder is 0, so 2 is a divisor of 3676)
3676 / 3 = 1225.3333333333 (the remainder is 1, so 3 is not a divisor of 3676)
...
3676 / 3675 = 1.0002721088435 (the remainder is 1, so 3675 is not a divisor of 3676)
3676 / 3676 = 1 (the remainder is 0, so 3676 is a divisor of 3676)

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 3676 (i.e. 60.630025564896). 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 $\frac{N}{d} = D$ )

3676 / 1 = 3676 (the remainder is 0, so 1 and 3676 are divisors of 3676)
3676 / 2 = 1838 (the remainder is 0, so 2 and 1838 are divisors of 3676)
3676 / 3 = 1225.3333333333 (the remainder is 1, so 3 is not a divisor of 3676)
...
3676 / 59 = 62.305084745763 (the remainder is 18, so 59 is not a divisor of 3676)
3676 / 60 = 61.266666666667 (the remainder is 16, so 60 is not a divisor of 3676)