What are the divisors of 602?

1, 2, 7, 14, 43, 86, 301, 602

There is a total of 8 positive divisors.
The sum of these divisors is 1056.
The arithmetic mean is 132.

4 even divisors

2, 14, 86, 602

4 odd divisors

1, 7, 43, 301

How to compute the divisors of 602?

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 602 by each of the numbers from 1 to 602 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)

602 / 1 = 602 (the remainder is 0, so 1 is a divisor of 602)
602 / 2 = 301 (the remainder is 0, so 2 is a divisor of 602)
602 / 3 = 200.66666666667 (the remainder is 2, so 3 is not a divisor of 602)
...
602 / 601 = 1.0016638935108 (the remainder is 1, so 601 is not a divisor of 602)
602 / 602 = 1 (the remainder is 0, so 602 is a divisor of 602)

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 602 (i.e. 24.535688292771). 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 $\frac{N}{d} = D$ )

602 / 1 = 602 (the remainder is 0, so 1 and 602 are divisors of 602)
602 / 2 = 301 (the remainder is 0, so 2 and 301 are divisors of 602)
602 / 3 = 200.66666666667 (the remainder is 2, so 3 is not a divisor of 602)
...
602 / 23 = 26.173913043478 (the remainder is 4, so 23 is not a divisor of 602)
602 / 24 = 25.083333333333 (the remainder is 2, so 24 is not a divisor of 602)