What are the divisors of 4732?

1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 169, 182, 338, 364, 676, 1183, 2366, 4732

There is a total of 18 positive divisors.
The sum of these divisors is 10248.
The arithmetic mean is 569.33333333333.

12 even divisors

2, 4, 14, 26, 28, 52, 182, 338, 364, 676, 2366, 4732

6 odd divisors

1, 7, 13, 91, 169, 1183

How to compute the divisors of 4732?

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 4732 by each of the numbers from 1 to 4732 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)

4732 / 1 = 4732 (the remainder is 0, so 1 is a divisor of 4732)
4732 / 2 = 2366 (the remainder is 0, so 2 is a divisor of 4732)
4732 / 3 = 1577.3333333333 (the remainder is 1, so 3 is not a divisor of 4732)
...
4732 / 4731 = 1.000211371803 (the remainder is 1, so 4731 is not a divisor of 4732)
4732 / 4732 = 1 (the remainder is 0, so 4732 is a divisor of 4732)

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 4732 (i.e. 68.789534087679). 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 $\frac{N}{d} = D$ )

4732 / 1 = 4732 (the remainder is 0, so 1 and 4732 are divisors of 4732)
4732 / 2 = 2366 (the remainder is 0, so 2 and 2366 are divisors of 4732)
4732 / 3 = 1577.3333333333 (the remainder is 1, so 3 is not a divisor of 4732)
...
4732 / 67 = 70.626865671642 (the remainder is 42, so 67 is not a divisor of 4732)
4732 / 68 = 69.588235294118 (the remainder is 40, so 68 is not a divisor of 4732)