What are the divisors of 7062?

1, 2, 3, 6, 11, 22, 33, 66, 107, 214, 321, 642, 1177, 2354, 3531, 7062

There is a total of 16 positive divisors.
The sum of these divisors is 15552.
The arithmetic mean is 972.

8 even divisors

2, 6, 22, 66, 214, 642, 2354, 7062

8 odd divisors

1, 3, 11, 33, 107, 321, 1177, 3531

How to compute the divisors of 7062?

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 7062 by each of the numbers from 1 to 7062 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)

7062 / 1 = 7062 (the remainder is 0, so 1 is a divisor of 7062)
7062 / 2 = 3531 (the remainder is 0, so 2 is a divisor of 7062)
7062 / 3 = 2354 (the remainder is 0, so 3 is a divisor of 7062)
...
7062 / 7061 = 1.0001416229996 (the remainder is 1, so 7061 is not a divisor of 7062)
7062 / 7062 = 1 (the remainder is 0, so 7062 is a divisor of 7062)

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 7062 (i.e. 84.035706696618). 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 $\frac{N}{d} = D$ )

7062 / 1 = 7062 (the remainder is 0, so 1 and 7062 are divisors of 7062)
7062 / 2 = 3531 (the remainder is 0, so 2 and 3531 are divisors of 7062)
7062 / 3 = 2354 (the remainder is 0, so 3 and 2354 are divisors of 7062)
...
7062 / 83 = 85.084337349398 (the remainder is 7, so 83 is not a divisor of 7062)
7062 / 84 = 84.071428571429 (the remainder is 6, so 84 is not a divisor of 7062)