What are the divisors of 7054?

1, 2, 3527, 7054

There is a total of 4 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 2646.

2 even divisors

2, 7054

2 odd divisors

1, 3527

How to compute the divisors of 7054?

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 7054 by each of the numbers from 1 to 7054 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)

7054 / 1 = 7054 (the remainder is 0, so 1 is a divisor of 7054)
7054 / 2 = 3527 (the remainder is 0, so 2 is a divisor of 7054)
7054 / 3 = 2351.3333333333 (the remainder is 1, so 3 is not a divisor of 7054)
...
7054 / 7053 = 1.0001417836382 (the remainder is 1, so 7053 is not a divisor of 7054)
7054 / 7054 = 1 (the remainder is 0, so 7054 is a divisor of 7054)

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 7054 (i.e. 83.988094394384). 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 $\frac{N}{d} = D$ )

7054 / 1 = 7054 (the remainder is 0, so 1 and 7054 are divisors of 7054)
7054 / 2 = 3527 (the remainder is 0, so 2 and 3527 are divisors of 7054)
7054 / 3 = 2351.3333333333 (the remainder is 1, so 3 is not a divisor of 7054)
...
7054 / 82 = 86.024390243902 (the remainder is 2, so 82 is not a divisor of 7054)
7054 / 83 = 84.987951807229 (the remainder is 82, so 83 is not a divisor of 7054)