What are the divisors of 1546?

1, 2, 773, 1546

There is a total of 4 positive divisors.
The sum of these divisors is 2322.
The arithmetic mean is 580.5.

2 even divisors

2, 1546

2 odd divisors

1, 773

How to compute the divisors of 1546?

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 1546 by each of the numbers from 1 to 1546 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)

1546 / 1 = 1546 (the remainder is 0, so 1 is a divisor of 1546)
1546 / 2 = 773 (the remainder is 0, so 2 is a divisor of 1546)
1546 / 3 = 515.33333333333 (the remainder is 1, so 3 is not a divisor of 1546)
...
1546 / 1545 = 1.0006472491909 (the remainder is 1, so 1545 is not a divisor of 1546)
1546 / 1546 = 1 (the remainder is 0, so 1546 is a divisor of 1546)

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 1546 (i.e. 39.319206502675). 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 $\frac{N}{d} = D$ )

1546 / 1 = 1546 (the remainder is 0, so 1 and 1546 are divisors of 1546)
1546 / 2 = 773 (the remainder is 0, so 2 and 773 are divisors of 1546)
1546 / 3 = 515.33333333333 (the remainder is 1, so 3 is not a divisor of 1546)
...
1546 / 38 = 40.684210526316 (the remainder is 26, so 38 is not a divisor of 1546)
1546 / 39 = 39.641025641026 (the remainder is 25, so 39 is not a divisor of 1546)