What are the divisors of 7091?

1, 7, 1013, 7091

4 odd divisors

1, 7, 1013, 7091

How to compute the divisors of 7091?

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 7091 by each of the numbers from 1 to 7091 to determine which ones have a remainder equal to 0.

Remainder = N ( M × N M )

(where N M is the integer part of the quotient)

  • 7091 / 1 = 7091 (the remainder is 0, so 1 is a divisor of 7091)
  • 7091 / 2 = 3545.5 (the remainder is 1, so 2 is not a divisor of 7091)
  • 7091 / 3 = 2363.6666666667 (the remainder is 2, so 3 is not a divisor of 7091)
  • ...
  • 7091 / 7090 = 1.0001410437236 (the remainder is 1, so 7090 is not a divisor of 7091)
  • 7091 / 7091 = 1 (the remainder is 0, so 7091 is a divisor of 7091)

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 7091 (i.e. 84.208075622235). 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 × d = N

(thus, if N D = d , then N d = D )

  • 7091 / 1 = 7091 (the remainder is 0, so 1 and 7091 are divisors of 7091)
  • 7091 / 2 = 3545.5 (the remainder is 1, so 2 is not a divisor of 7091)
  • 7091 / 3 = 2363.6666666667 (the remainder is 2, so 3 is not a divisor of 7091)
  • ...
  • 7091 / 83 = 85.433734939759 (the remainder is 36, so 83 is not a divisor of 7091)
  • 7091 / 84 = 84.416666666667 (the remainder is 35, so 84 is not a divisor of 7091)