What are the divisors of 3662?

1, 2, 1831, 3662

There is a total of 4 positive divisors.
The sum of these divisors is 5496.
The arithmetic mean is 1374.

2 even divisors

2, 3662

2 odd divisors

1, 1831

How to compute the divisors of 3662?

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 3662 by each of the numbers from 1 to 3662 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)

3662 / 1 = 3662 (the remainder is 0, so 1 is a divisor of 3662)
3662 / 2 = 1831 (the remainder is 0, so 2 is a divisor of 3662)
3662 / 3 = 1220.6666666667 (the remainder is 2, so 3 is not a divisor of 3662)
...
3662 / 3661 = 1.0002731494127 (the remainder is 1, so 3661 is not a divisor of 3662)
3662 / 3662 = 1 (the remainder is 0, so 3662 is a divisor of 3662)

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 3662 (i.e. 60.514461081629). 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 $\frac{N}{d} = D$ )

3662 / 1 = 3662 (the remainder is 0, so 1 and 3662 are divisors of 3662)
3662 / 2 = 1831 (the remainder is 0, so 2 and 1831 are divisors of 3662)
3662 / 3 = 1220.6666666667 (the remainder is 2, so 3 is not a divisor of 3662)
...
3662 / 59 = 62.067796610169 (the remainder is 4, so 59 is not a divisor of 3662)
3662 / 60 = 61.033333333333 (the remainder is 2, so 60 is not a divisor of 3662)