What are the divisors of 7100?

1, 2, 4, 5, 10, 20, 25, 50, 71, 100, 142, 284, 355, 710, 1420, 1775, 3550, 7100

There is a total of 18 positive divisors.
The sum of these divisors is 15624.
The arithmetic mean is 868.

12 even divisors

2, 4, 10, 20, 50, 100, 142, 284, 710, 1420, 3550, 7100

6 odd divisors

1, 5, 25, 71, 355, 1775

How to compute the divisors of 7100?

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 7100 by each of the numbers from 1 to 7100 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)

7100 / 1 = 7100 (the remainder is 0, so 1 is a divisor of 7100)
7100 / 2 = 3550 (the remainder is 0, so 2 is a divisor of 7100)
7100 / 3 = 2366.6666666667 (the remainder is 2, so 3 is not a divisor of 7100)
...
7100 / 7099 = 1.0001408649106 (the remainder is 1, so 7099 is not a divisor of 7100)
7100 / 7100 = 1 (the remainder is 0, so 7100 is a divisor of 7100)

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 7100 (i.e. 84.261497731764). 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 $\frac{N}{d} = D$ )

7100 / 1 = 7100 (the remainder is 0, so 1 and 7100 are divisors of 7100)
7100 / 2 = 3550 (the remainder is 0, so 2 and 3550 are divisors of 7100)
7100 / 3 = 2366.6666666667 (the remainder is 2, so 3 is not a divisor of 7100)
...
7100 / 83 = 85.542168674699 (the remainder is 45, so 83 is not a divisor of 7100)
7100 / 84 = 84.52380952381 (the remainder is 44, so 84 is not a divisor of 7100)