What are the divisors of 1468?

1, 2, 4, 367, 734, 1468

There is a total of 6 positive divisors.
The sum of these divisors is 2576.
The arithmetic mean is 429.33333333333.

4 even divisors

2, 4, 734, 1468

2 odd divisors

1, 367

How to compute the divisors of 1468?

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 1468 by each of the numbers from 1 to 1468 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)

1468 / 1 = 1468 (the remainder is 0, so 1 is a divisor of 1468)
1468 / 2 = 734 (the remainder is 0, so 2 is a divisor of 1468)
1468 / 3 = 489.33333333333 (the remainder is 1, so 3 is not a divisor of 1468)
...
1468 / 1467 = 1.0006816632584 (the remainder is 1, so 1467 is not a divisor of 1468)
1468 / 1468 = 1 (the remainder is 0, so 1468 is a divisor of 1468)

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 1468 (i.e. 38.314488121336). 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 $\frac{N}{d} = D$ )

1468 / 1 = 1468 (the remainder is 0, so 1 and 1468 are divisors of 1468)
1468 / 2 = 734 (the remainder is 0, so 2 and 734 are divisors of 1468)
1468 / 3 = 489.33333333333 (the remainder is 1, so 3 is not a divisor of 1468)
...
1468 / 37 = 39.675675675676 (the remainder is 25, so 37 is not a divisor of 1468)
1468 / 38 = 38.631578947368 (the remainder is 24, so 38 is not a divisor of 1468)