What are the divisors of 7097?

1, 47, 151, 7097

There is a total of 4 positive divisors.
The sum of these divisors is 7296.
The arithmetic mean is 1824.

4 odd divisors

1, 47, 151, 7097

How to compute the divisors of 7097?

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 7097 by each of the numbers from 1 to 7097 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)

7097 / 1 = 7097 (the remainder is 0, so 1 is a divisor of 7097)
7097 / 2 = 3548.5 (the remainder is 1, so 2 is not a divisor of 7097)
7097 / 3 = 2365.6666666667 (the remainder is 2, so 3 is not a divisor of 7097)
...
7097 / 7096 = 1.0001409244645 (the remainder is 1, so 7096 is not a divisor of 7097)
7097 / 7097 = 1 (the remainder is 0, so 7097 is a divisor of 7097)

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 7097 (i.e. 84.243694126029). 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 $\frac{N}{d} = D$ )

7097 / 1 = 7097 (the remainder is 0, so 1 and 7097 are divisors of 7097)
7097 / 2 = 3548.5 (the remainder is 1, so 2 is not a divisor of 7097)
7097 / 3 = 2365.6666666667 (the remainder is 2, so 3 is not a divisor of 7097)
...
7097 / 83 = 85.506024096386 (the remainder is 42, so 83 is not a divisor of 7097)
7097 / 84 = 84.488095238095 (the remainder is 41, so 84 is not a divisor of 7097)