What are the divisors of 4602?

1, 2, 3, 6, 13, 26, 39, 59, 78, 118, 177, 354, 767, 1534, 2301, 4602

There is a total of 16 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 630.

8 even divisors

2, 6, 26, 78, 118, 354, 1534, 4602

8 odd divisors

1, 3, 13, 39, 59, 177, 767, 2301

How to compute the divisors of 4602?

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 4602 by each of the numbers from 1 to 4602 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)

4602 / 1 = 4602 (the remainder is 0, so 1 is a divisor of 4602)
4602 / 2 = 2301 (the remainder is 0, so 2 is a divisor of 4602)
4602 / 3 = 1534 (the remainder is 0, so 3 is a divisor of 4602)
...
4602 / 4601 = 1.0002173440556 (the remainder is 1, so 4601 is not a divisor of 4602)
4602 / 4602 = 1 (the remainder is 0, so 4602 is a divisor of 4602)

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 4602 (i.e. 67.838042424587). 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 $\frac{N}{d} = D$ )

4602 / 1 = 4602 (the remainder is 0, so 1 and 4602 are divisors of 4602)
4602 / 2 = 2301 (the remainder is 0, so 2 and 2301 are divisors of 4602)
4602 / 3 = 1534 (the remainder is 0, so 3 and 1534 are divisors of 4602)
...
4602 / 66 = 69.727272727273 (the remainder is 48, so 66 is not a divisor of 4602)
4602 / 67 = 68.686567164179 (the remainder is 46, so 67 is not a divisor of 4602)