What are the divisors of 1434?

1, 2, 3, 6, 239, 478, 717, 1434

There is a total of 8 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 360.

4 even divisors

2, 6, 478, 1434

4 odd divisors

1, 3, 239, 717

How to compute the divisors of 1434?

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 1434 by each of the numbers from 1 to 1434 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)

1434 / 1 = 1434 (the remainder is 0, so 1 is a divisor of 1434)
1434 / 2 = 717 (the remainder is 0, so 2 is a divisor of 1434)
1434 / 3 = 478 (the remainder is 0, so 3 is a divisor of 1434)
...
1434 / 1433 = 1.0006978367062 (the remainder is 1, so 1433 is not a divisor of 1434)
1434 / 1434 = 1 (the remainder is 0, so 1434 is a divisor of 1434)

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 1434 (i.e. 37.868192457523). 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 $\frac{N}{d} = D$ )

1434 / 1 = 1434 (the remainder is 0, so 1 and 1434 are divisors of 1434)
1434 / 2 = 717 (the remainder is 0, so 2 and 717 are divisors of 1434)
1434 / 3 = 478 (the remainder is 0, so 3 and 478 are divisors of 1434)
...
1434 / 36 = 39.833333333333 (the remainder is 30, so 36 is not a divisor of 1434)
1434 / 37 = 38.756756756757 (the remainder is 28, so 37 is not a divisor of 1434)