What are the divisors of 1802?

1, 2, 17, 34, 53, 106, 901, 1802

There is a total of 8 positive divisors.
The sum of these divisors is 2916.
The arithmetic mean is 364.5.

4 even divisors

2, 34, 106, 1802

4 odd divisors

1, 17, 53, 901

How to compute the divisors of 1802?

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 1802 by each of the numbers from 1 to 1802 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)

1802 / 1 = 1802 (the remainder is 0, so 1 is a divisor of 1802)
1802 / 2 = 901 (the remainder is 0, so 2 is a divisor of 1802)
1802 / 3 = 600.66666666667 (the remainder is 2, so 3 is not a divisor of 1802)
...
1802 / 1801 = 1.000555247085 (the remainder is 1, so 1801 is not a divisor of 1802)
1802 / 1802 = 1 (the remainder is 0, so 1802 is a divisor of 1802)

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 1802 (i.e. 42.449970553582). 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 $\frac{N}{d} = D$ )

1802 / 1 = 1802 (the remainder is 0, so 1 and 1802 are divisors of 1802)
1802 / 2 = 901 (the remainder is 0, so 2 and 901 are divisors of 1802)
1802 / 3 = 600.66666666667 (the remainder is 2, so 3 is not a divisor of 1802)
...
1802 / 41 = 43.951219512195 (the remainder is 39, so 41 is not a divisor of 1802)
1802 / 42 = 42.904761904762 (the remainder is 38, so 42 is not a divisor of 1802)