What are the divisors of 1418?

1, 2, 709, 1418

There is a total of 4 positive divisors.
The sum of these divisors is 2130.
The arithmetic mean is 532.5.

2 even divisors

2, 1418

2 odd divisors

1, 709

How to compute the divisors of 1418?

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 1418 by each of the numbers from 1 to 1418 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)

1418 / 1 = 1418 (the remainder is 0, so 1 is a divisor of 1418)
1418 / 2 = 709 (the remainder is 0, so 2 is a divisor of 1418)
1418 / 3 = 472.66666666667 (the remainder is 2, so 3 is not a divisor of 1418)
...
1418 / 1417 = 1.000705716302 (the remainder is 1, so 1417 is not a divisor of 1418)
1418 / 1418 = 1 (the remainder is 0, so 1418 is a divisor of 1418)

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 1418 (i.e. 37.656340767525). 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 $\frac{N}{d} = D$ )

1418 / 1 = 1418 (the remainder is 0, so 1 and 1418 are divisors of 1418)
1418 / 2 = 709 (the remainder is 0, so 2 and 709 are divisors of 1418)
1418 / 3 = 472.66666666667 (the remainder is 2, so 3 is not a divisor of 1418)
...
1418 / 36 = 39.388888888889 (the remainder is 14, so 36 is not a divisor of 1418)
1418 / 37 = 38.324324324324 (the remainder is 12, so 37 is not a divisor of 1418)