What are the divisors of 1422?

1, 2, 3, 6, 9, 18, 79, 158, 237, 474, 711, 1422

There is a total of 12 positive divisors.
The sum of these divisors is 3120.
The arithmetic mean is 260.

6 even divisors

2, 6, 18, 158, 474, 1422

6 odd divisors

1, 3, 9, 79, 237, 711

How to compute the divisors of 1422?

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 1422 by each of the numbers from 1 to 1422 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)

1422 / 1 = 1422 (the remainder is 0, so 1 is a divisor of 1422)
1422 / 2 = 711 (the remainder is 0, so 2 is a divisor of 1422)
1422 / 3 = 474 (the remainder is 0, so 3 is a divisor of 1422)
...
1422 / 1421 = 1.0007037297678 (the remainder is 1, so 1421 is not a divisor of 1422)
1422 / 1422 = 1 (the remainder is 0, so 1422 is a divisor of 1422)

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 1422 (i.e. 37.70941526993). 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 $\frac{N}{d} = D$ )

1422 / 1 = 1422 (the remainder is 0, so 1 and 1422 are divisors of 1422)
1422 / 2 = 711 (the remainder is 0, so 2 and 711 are divisors of 1422)
1422 / 3 = 474 (the remainder is 0, so 3 and 474 are divisors of 1422)
...
1422 / 36 = 39.5 (the remainder is 18, so 36 is not a divisor of 1422)
1422 / 37 = 38.432432432432 (the remainder is 16, so 37 is not a divisor of 1422)