What are the divisors of 5513?

1, 37, 149, 5513

There is a total of 4 positive divisors.
The sum of these divisors is 5700.
The arithmetic mean is 1425.

4 odd divisors

1, 37, 149, 5513

How to compute the divisors of 5513?

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 5513 by each of the numbers from 1 to 5513 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)

5513 / 1 = 5513 (the remainder is 0, so 1 is a divisor of 5513)
5513 / 2 = 2756.5 (the remainder is 1, so 2 is not a divisor of 5513)
5513 / 3 = 1837.6666666667 (the remainder is 2, so 3 is not a divisor of 5513)
...
5513 / 5512 = 1.0001814223512 (the remainder is 1, so 5512 is not a divisor of 5513)
5513 / 5513 = 1 (the remainder is 0, so 5513 is a divisor of 5513)

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 5513 (i.e. 74.249579123386). 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 $\frac{N}{d} = D$ )

5513 / 1 = 5513 (the remainder is 0, so 1 and 5513 are divisors of 5513)
5513 / 2 = 2756.5 (the remainder is 1, so 2 is not a divisor of 5513)
5513 / 3 = 1837.6666666667 (the remainder is 2, so 3 is not a divisor of 5513)
...
5513 / 73 = 75.520547945205 (the remainder is 38, so 73 is not a divisor of 5513)
5513 / 74 = 74.5 (the remainder is 37, so 74 is not a divisor of 5513)