What are the divisors of 4628?

1, 2, 4, 13, 26, 52, 89, 178, 356, 1157, 2314, 4628

There is a total of 12 positive divisors.
The sum of these divisors is 8820.
The arithmetic mean is 735.

8 even divisors

2, 4, 26, 52, 178, 356, 2314, 4628

4 odd divisors

1, 13, 89, 1157

How to compute the divisors of 4628?

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 4628 by each of the numbers from 1 to 4628 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)

4628 / 1 = 4628 (the remainder is 0, so 1 is a divisor of 4628)
4628 / 2 = 2314 (the remainder is 0, so 2 is a divisor of 4628)
4628 / 3 = 1542.6666666667 (the remainder is 2, so 3 is not a divisor of 4628)
...
4628 / 4627 = 1.0002161227577 (the remainder is 1, so 4627 is not a divisor of 4628)
4628 / 4628 = 1 (the remainder is 0, so 4628 is a divisor of 4628)

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 4628 (i.e. 68.02940540678). 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 $\frac{N}{d} = D$ )

4628 / 1 = 4628 (the remainder is 0, so 1 and 4628 are divisors of 4628)
4628 / 2 = 2314 (the remainder is 0, so 2 and 2314 are divisors of 4628)
4628 / 3 = 1542.6666666667 (the remainder is 2, so 3 is not a divisor of 4628)
...
4628 / 67 = 69.074626865672 (the remainder is 5, so 67 is not a divisor of 4628)
4628 / 68 = 68.058823529412 (the remainder is 4, so 68 is not a divisor of 4628)