What are the divisors of 3622?

1, 2, 1811, 3622

There is a total of 4 positive divisors.
The sum of these divisors is 5436.
The arithmetic mean is 1359.

2 even divisors

2, 3622

2 odd divisors

1, 1811

How to compute the divisors of 3622?

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 3622 by each of the numbers from 1 to 3622 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)

3622 / 1 = 3622 (the remainder is 0, so 1 is a divisor of 3622)
3622 / 2 = 1811 (the remainder is 0, so 2 is a divisor of 3622)
3622 / 3 = 1207.3333333333 (the remainder is 1, so 3 is not a divisor of 3622)
...
3622 / 3621 = 1.0002761668048 (the remainder is 1, so 3621 is not a divisor of 3622)
3622 / 3622 = 1 (the remainder is 0, so 3622 is a divisor of 3622)

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 3622 (i.e. 60.183054093324). 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 $\frac{N}{d} = D$ )

3622 / 1 = 3622 (the remainder is 0, so 1 and 3622 are divisors of 3622)
3622 / 2 = 1811 (the remainder is 0, so 2 and 1811 are divisors of 3622)
3622 / 3 = 1207.3333333333 (the remainder is 1, so 3 is not a divisor of 3622)
...
3622 / 59 = 61.389830508475 (the remainder is 23, so 59 is not a divisor of 3622)
3622 / 60 = 60.366666666667 (the remainder is 22, so 60 is not a divisor of 3622)