What are the divisors of 5477?

1, 5477

There is a total of 2 positive divisors.
The sum of these divisors is 5478.
The arithmetic mean is 2739.

2 odd divisors

1, 5477

How to compute the divisors of 5477?

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 5477 by each of the numbers from 1 to 5477 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)

5477 / 1 = 5477 (the remainder is 0, so 1 is a divisor of 5477)
5477 / 2 = 2738.5 (the remainder is 1, so 2 is not a divisor of 5477)
5477 / 3 = 1825.6666666667 (the remainder is 2, so 3 is not a divisor of 5477)
...
5477 / 5476 = 1.0001826150475 (the remainder is 1, so 5476 is not a divisor of 5477)
5477 / 5477 = 1 (the remainder is 0, so 5477 is a divisor of 5477)

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 5477 (i.e. 74.006756448314). 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 $\frac{N}{d} = D$ )

5477 / 1 = 5477 (the remainder is 0, so 1 and 5477 are divisors of 5477)
5477 / 2 = 2738.5 (the remainder is 1, so 2 is not a divisor of 5477)
5477 / 3 = 1825.6666666667 (the remainder is 2, so 3 is not a divisor of 5477)
...
5477 / 73 = 75.027397260274 (the remainder is 2, so 73 is not a divisor of 5477)
5477 / 74 = 74.013513513514 (the remainder is 1, so 74 is not a divisor of 5477)