What are the divisors of 547?

1, 547

There is a total of 2 positive divisors.
The sum of these divisors is 548.
The arithmetic mean is 274.

2 odd divisors

1, 547

How to compute the divisors of 547?

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 547 by each of the numbers from 1 to 547 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)

547 / 1 = 547 (the remainder is 0, so 1 is a divisor of 547)
547 / 2 = 273.5 (the remainder is 1, so 2 is not a divisor of 547)
547 / 3 = 182.33333333333 (the remainder is 1, so 3 is not a divisor of 547)
...
547 / 546 = 1.0018315018315 (the remainder is 1, so 546 is not a divisor of 547)
547 / 547 = 1 (the remainder is 0, so 547 is a divisor of 547)

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 547 (i.e. 23.388031127053). 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 $\frac{N}{d} = D$ )

547 / 1 = 547 (the remainder is 0, so 1 and 547 are divisors of 547)
547 / 2 = 273.5 (the remainder is 1, so 2 is not a divisor of 547)
547 / 3 = 182.33333333333 (the remainder is 1, so 3 is not a divisor of 547)
...
547 / 22 = 24.863636363636 (the remainder is 19, so 22 is not a divisor of 547)
547 / 23 = 23.782608695652 (the remainder is 18, so 23 is not a divisor of 547)