What are the divisors of 3602?

1, 2, 1801, 3602

There is a total of 4 positive divisors.
The sum of these divisors is 5406.
The arithmetic mean is 1351.5.

2 even divisors

2, 3602

2 odd divisors

1, 1801

How to compute the divisors of 3602?

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 3602 by each of the numbers from 1 to 3602 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)

3602 / 1 = 3602 (the remainder is 0, so 1 is a divisor of 3602)
3602 / 2 = 1801 (the remainder is 0, so 2 is a divisor of 3602)
3602 / 3 = 1200.6666666667 (the remainder is 2, so 3 is not a divisor of 3602)
...
3602 / 3601 = 1.0002777006387 (the remainder is 1, so 3601 is not a divisor of 3602)
3602 / 3602 = 1 (the remainder is 0, so 3602 is a divisor of 3602)

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 3602 (i.e. 60.016664352495). 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 $\frac{N}{d} = D$ )

3602 / 1 = 3602 (the remainder is 0, so 1 and 3602 are divisors of 3602)
3602 / 2 = 1801 (the remainder is 0, so 2 and 1801 are divisors of 3602)
3602 / 3 = 1200.6666666667 (the remainder is 2, so 3 is not a divisor of 3602)
...
3602 / 59 = 61.050847457627 (the remainder is 3, so 59 is not a divisor of 3602)
3602 / 60 = 60.033333333333 (the remainder is 2, so 60 is not a divisor of 3602)