What are the divisors of 436?

1, 2, 4, 109, 218, 436

There is a total of 6 positive divisors.
The sum of these divisors is 770.
The arithmetic mean is 128.33333333333.

4 even divisors

2, 4, 218, 436

2 odd divisors

1, 109

How to compute the divisors of 436?

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 436 by each of the numbers from 1 to 436 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)

436 / 1 = 436 (the remainder is 0, so 1 is a divisor of 436)
436 / 2 = 218 (the remainder is 0, so 2 is a divisor of 436)
436 / 3 = 145.33333333333 (the remainder is 1, so 3 is not a divisor of 436)
...
436 / 435 = 1.0022988505747 (the remainder is 1, so 435 is not a divisor of 436)
436 / 436 = 1 (the remainder is 0, so 436 is a divisor of 436)

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 436 (i.e. 20.880613017821). 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 $\frac{N}{d} = D$ )

436 / 1 = 436 (the remainder is 0, so 1 and 436 are divisors of 436)
436 / 2 = 218 (the remainder is 0, so 2 and 218 are divisors of 436)
436 / 3 = 145.33333333333 (the remainder is 1, so 3 is not a divisor of 436)
...
436 / 19 = 22.947368421053 (the remainder is 18, so 19 is not a divisor of 436)
436 / 20 = 21.8 (the remainder is 16, so 20 is not a divisor of 436)