What are the divisors of 4132?

1, 2, 4, 1033, 2066, 4132

There is a total of 6 positive divisors.
The sum of these divisors is 7238.
The arithmetic mean is 1206.3333333333.

4 even divisors

2, 4, 2066, 4132

2 odd divisors

1, 1033

How to compute the divisors of 4132?

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 4132 by each of the numbers from 1 to 4132 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)

4132 / 1 = 4132 (the remainder is 0, so 1 is a divisor of 4132)
4132 / 2 = 2066 (the remainder is 0, so 2 is a divisor of 4132)
4132 / 3 = 1377.3333333333 (the remainder is 1, so 3 is not a divisor of 4132)
...
4132 / 4131 = 1.0002420721375 (the remainder is 1, so 4131 is not a divisor of 4132)
4132 / 4132 = 1 (the remainder is 0, so 4132 is a divisor of 4132)

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 4132 (i.e. 64.280634719953). 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 $\frac{N}{d} = D$ )

4132 / 1 = 4132 (the remainder is 0, so 1 and 4132 are divisors of 4132)
4132 / 2 = 2066 (the remainder is 0, so 2 and 2066 are divisors of 4132)
4132 / 3 = 1377.3333333333 (the remainder is 1, so 3 is not a divisor of 4132)
...
4132 / 63 = 65.587301587302 (the remainder is 37, so 63 is not a divisor of 4132)
4132 / 64 = 64.5625 (the remainder is 36, so 64 is not a divisor of 4132)