What are the divisors of 1432?

1, 2, 4, 8, 179, 358, 716, 1432

There is a total of 8 positive divisors.
The sum of these divisors is 2700.
The arithmetic mean is 337.5.

6 even divisors

2, 4, 8, 358, 716, 1432

2 odd divisors

1, 179

How to compute the divisors of 1432?

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 1432 by each of the numbers from 1 to 1432 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)

1432 / 1 = 1432 (the remainder is 0, so 1 is a divisor of 1432)
1432 / 2 = 716 (the remainder is 0, so 2 is a divisor of 1432)
1432 / 3 = 477.33333333333 (the remainder is 1, so 3 is not a divisor of 1432)
...
1432 / 1431 = 1.0006988120196 (the remainder is 1, so 1431 is not a divisor of 1432)
1432 / 1432 = 1 (the remainder is 0, so 1432 is a divisor of 1432)

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 1432 (i.e. 37.841775856849). 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 $\frac{N}{d} = D$ )

1432 / 1 = 1432 (the remainder is 0, so 1 and 1432 are divisors of 1432)
1432 / 2 = 716 (the remainder is 0, so 2 and 716 are divisors of 1432)
1432 / 3 = 477.33333333333 (the remainder is 1, so 3 is not a divisor of 1432)
...
1432 / 36 = 39.777777777778 (the remainder is 28, so 36 is not a divisor of 1432)
1432 / 37 = 38.702702702703 (the remainder is 26, so 37 is not a divisor of 1432)