What are the divisors of 1454?

1, 2, 727, 1454

There is a total of 4 positive divisors.
The sum of these divisors is 2184.
The arithmetic mean is 546.

2 even divisors

2, 1454

2 odd divisors

1, 727

How to compute the divisors of 1454?

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 1454 by each of the numbers from 1 to 1454 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)

1454 / 1 = 1454 (the remainder is 0, so 1 is a divisor of 1454)
1454 / 2 = 727 (the remainder is 0, so 2 is a divisor of 1454)
1454 / 3 = 484.66666666667 (the remainder is 2, so 3 is not a divisor of 1454)
...
1454 / 1453 = 1.0006882312457 (the remainder is 1, so 1453 is not a divisor of 1454)
1454 / 1454 = 1 (the remainder is 0, so 1454 is a divisor of 1454)

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 1454 (i.e. 38.131351929875). 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 $\frac{N}{d} = D$ )

1454 / 1 = 1454 (the remainder is 0, so 1 and 1454 are divisors of 1454)
1454 / 2 = 727 (the remainder is 0, so 2 and 727 are divisors of 1454)
1454 / 3 = 484.66666666667 (the remainder is 2, so 3 is not a divisor of 1454)
...
1454 / 37 = 39.297297297297 (the remainder is 11, so 37 is not a divisor of 1454)
1454 / 38 = 38.263157894737 (the remainder is 10, so 38 is not a divisor of 1454)