What are the divisors of 1442?

1, 2, 7, 14, 103, 206, 721, 1442

There is a total of 8 positive divisors.
The sum of these divisors is 2496.
The arithmetic mean is 312.

4 even divisors

2, 14, 206, 1442

4 odd divisors

1, 7, 103, 721

How to compute the divisors of 1442?

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 1442 by each of the numbers from 1 to 1442 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)

1442 / 1 = 1442 (the remainder is 0, so 1 is a divisor of 1442)
1442 / 2 = 721 (the remainder is 0, so 2 is a divisor of 1442)
1442 / 3 = 480.66666666667 (the remainder is 2, so 3 is not a divisor of 1442)
...
1442 / 1441 = 1.000693962526 (the remainder is 1, so 1441 is not a divisor of 1442)
1442 / 1442 = 1 (the remainder is 0, so 1442 is a divisor of 1442)

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 1442 (i.e. 37.973675092095). 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 $\frac{N}{d} = D$ )

1442 / 1 = 1442 (the remainder is 0, so 1 and 1442 are divisors of 1442)
1442 / 2 = 721 (the remainder is 0, so 2 and 721 are divisors of 1442)
1442 / 3 = 480.66666666667 (the remainder is 2, so 3 is not a divisor of 1442)
...
1442 / 36 = 40.055555555556 (the remainder is 2, so 36 is not a divisor of 1442)
1442 / 37 = 38.972972972973 (the remainder is 36, so 37 is not a divisor of 1442)