What are the divisors of 1453?

1, 1453

There is a total of 2 positive divisors.
The sum of these divisors is 1454.
The arithmetic mean is 727.

2 odd divisors

1, 1453

How to compute the divisors of 1453?

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 1453 by each of the numbers from 1 to 1453 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)

1453 / 1 = 1453 (the remainder is 0, so 1 is a divisor of 1453)
1453 / 2 = 726.5 (the remainder is 1, so 2 is not a divisor of 1453)
1453 / 3 = 484.33333333333 (the remainder is 1, so 3 is not a divisor of 1453)
...
1453 / 1452 = 1.0006887052342 (the remainder is 1, so 1452 is not a divisor of 1453)
1453 / 1453 = 1 (the remainder is 0, so 1453 is a divisor of 1453)

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 1453 (i.e. 38.118237105092). 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 $\frac{N}{d} = D$ )

1453 / 1 = 1453 (the remainder is 0, so 1 and 1453 are divisors of 1453)
1453 / 2 = 726.5 (the remainder is 1, so 2 is not a divisor of 1453)
1453 / 3 = 484.33333333333 (the remainder is 1, so 3 is not a divisor of 1453)
...
1453 / 37 = 39.27027027027 (the remainder is 10, so 37 is not a divisor of 1453)
1453 / 38 = 38.236842105263 (the remainder is 9, so 38 is not a divisor of 1453)