What are the divisors of 7102?

1, 2, 53, 67, 106, 134, 3551, 7102

There is a total of 8 positive divisors.
The sum of these divisors is 11016.
The arithmetic mean is 1377.

4 even divisors

2, 106, 134, 7102

4 odd divisors

1, 53, 67, 3551

How to compute the divisors of 7102?

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 7102 by each of the numbers from 1 to 7102 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)

7102 / 1 = 7102 (the remainder is 0, so 1 is a divisor of 7102)
7102 / 2 = 3551 (the remainder is 0, so 2 is a divisor of 7102)
7102 / 3 = 2367.3333333333 (the remainder is 1, so 3 is not a divisor of 7102)
...
7102 / 7101 = 1.0001408252359 (the remainder is 1, so 7101 is not a divisor of 7102)
7102 / 7102 = 1 (the remainder is 0, so 7102 is a divisor of 7102)

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 7102 (i.e. 84.273364712701). 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 $\frac{N}{d} = D$ )

7102 / 1 = 7102 (the remainder is 0, so 1 and 7102 are divisors of 7102)
7102 / 2 = 3551 (the remainder is 0, so 2 and 3551 are divisors of 7102)
7102 / 3 = 2367.3333333333 (the remainder is 1, so 3 is not a divisor of 7102)
...
7102 / 83 = 85.566265060241 (the remainder is 47, so 83 is not a divisor of 7102)
7102 / 84 = 84.547619047619 (the remainder is 46, so 84 is not a divisor of 7102)