What are the divisors of 4156?

1, 2, 4, 1039, 2078, 4156

There is a total of 6 positive divisors.
The sum of these divisors is 7280.
The arithmetic mean is 1213.3333333333.

4 even divisors

2, 4, 2078, 4156

2 odd divisors

1, 1039

How to compute the divisors of 4156?

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 4156 by each of the numbers from 1 to 4156 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)

4156 / 1 = 4156 (the remainder is 0, so 1 is a divisor of 4156)
4156 / 2 = 2078 (the remainder is 0, so 2 is a divisor of 4156)
4156 / 3 = 1385.3333333333 (the remainder is 1, so 3 is not a divisor of 4156)
...
4156 / 4155 = 1.0002406738869 (the remainder is 1, so 4155 is not a divisor of 4156)
4156 / 4156 = 1 (the remainder is 0, so 4156 is a divisor of 4156)

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 4156 (i.e. 64.467045845145). 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 $\frac{N}{d} = D$ )

4156 / 1 = 4156 (the remainder is 0, so 1 and 4156 are divisors of 4156)
4156 / 2 = 2078 (the remainder is 0, so 2 and 2078 are divisors of 4156)
4156 / 3 = 1385.3333333333 (the remainder is 1, so 3 is not a divisor of 4156)
...
4156 / 63 = 65.968253968254 (the remainder is 61, so 63 is not a divisor of 4156)
4156 / 64 = 64.9375 (the remainder is 60, so 64 is not a divisor of 4156)