What are the divisors of 5154?

1, 2, 3, 6, 859, 1718, 2577, 5154

There is a total of 8 positive divisors.
The sum of these divisors is 10320.
The arithmetic mean is 1290.

4 even divisors

2, 6, 1718, 5154

4 odd divisors

1, 3, 859, 2577

How to compute the divisors of 5154?

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 5154 by each of the numbers from 1 to 5154 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)

5154 / 1 = 5154 (the remainder is 0, so 1 is a divisor of 5154)
5154 / 2 = 2577 (the remainder is 0, so 2 is a divisor of 5154)
5154 / 3 = 1718 (the remainder is 0, so 3 is a divisor of 5154)
...
5154 / 5153 = 1.0001940617116 (the remainder is 1, so 5153 is not a divisor of 5154)
5154 / 5154 = 1 (the remainder is 0, so 5154 is a divisor of 5154)

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 5154 (i.e. 71.79136438319). 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 $\frac{N}{d} = D$ )

5154 / 1 = 5154 (the remainder is 0, so 1 and 5154 are divisors of 5154)
5154 / 2 = 2577 (the remainder is 0, so 2 and 2577 are divisors of 5154)
5154 / 3 = 1718 (the remainder is 0, so 3 and 1718 are divisors of 5154)
...
5154 / 70 = 73.628571428571 (the remainder is 44, so 70 is not a divisor of 5154)
5154 / 71 = 72.591549295775 (the remainder is 42, so 71 is not a divisor of 5154)