What are the divisors of 5377?

1, 19, 283, 5377

There is a total of 4 positive divisors.
The sum of these divisors is 5680.
The arithmetic mean is 1420.

4 odd divisors

1, 19, 283, 5377

How to compute the divisors of 5377?

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 5377 by each of the numbers from 1 to 5377 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)

5377 / 1 = 5377 (the remainder is 0, so 1 is a divisor of 5377)
5377 / 2 = 2688.5 (the remainder is 1, so 2 is not a divisor of 5377)
5377 / 3 = 1792.3333333333 (the remainder is 1, so 3 is not a divisor of 5377)
...
5377 / 5376 = 1.0001860119048 (the remainder is 1, so 5376 is not a divisor of 5377)
5377 / 5377 = 1 (the remainder is 0, so 5377 is a divisor of 5377)

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 5377 (i.e. 73.328030111275). 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 $\frac{N}{d} = D$ )

5377 / 1 = 5377 (the remainder is 0, so 1 and 5377 are divisors of 5377)
5377 / 2 = 2688.5 (the remainder is 1, so 2 is not a divisor of 5377)
5377 / 3 = 1792.3333333333 (the remainder is 1, so 3 is not a divisor of 5377)
...
5377 / 72 = 74.680555555556 (the remainder is 49, so 72 is not a divisor of 5377)
5377 / 73 = 73.657534246575 (the remainder is 48, so 73 is not a divisor of 5377)