What are the divisors of 1426?

1, 2, 23, 31, 46, 62, 713, 1426

There is a total of 8 positive divisors.
The sum of these divisors is 2304.
The arithmetic mean is 288.

4 even divisors

2, 46, 62, 1426

4 odd divisors

1, 23, 31, 713

How to compute the divisors of 1426?

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 1426 by each of the numbers from 1 to 1426 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)

1426 / 1 = 1426 (the remainder is 0, so 1 is a divisor of 1426)
1426 / 2 = 713 (the remainder is 0, so 2 is a divisor of 1426)
1426 / 3 = 475.33333333333 (the remainder is 1, so 3 is not a divisor of 1426)
...
1426 / 1425 = 1.000701754386 (the remainder is 1, so 1425 is not a divisor of 1426)
1426 / 1426 = 1 (the remainder is 0, so 1426 is a divisor of 1426)

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 1426 (i.e. 37.762415176998). 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 $\frac{N}{d} = D$ )

1426 / 1 = 1426 (the remainder is 0, so 1 and 1426 are divisors of 1426)
1426 / 2 = 713 (the remainder is 0, so 2 and 713 are divisors of 1426)
1426 / 3 = 475.33333333333 (the remainder is 1, so 3 is not a divisor of 1426)
...
1426 / 36 = 39.611111111111 (the remainder is 22, so 36 is not a divisor of 1426)
1426 / 37 = 38.540540540541 (the remainder is 20, so 37 is not a divisor of 1426)