What are the divisors of 8240?

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 103, 206, 412, 515, 824, 1030, 1648, 2060, 4120, 8240

16 even divisors

2, 4, 8, 10, 16, 20, 40, 80, 206, 412, 824, 1030, 1648, 2060, 4120, 8240

4 odd divisors

1, 5, 103, 515

How to compute the divisors of 8240?

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 8240 by each of the numbers from 1 to 8240 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)

  • 8240 / 1 = 8240 (the remainder is 0, so 1 is a divisor of 8240)
  • 8240 / 2 = 4120 (the remainder is 0, so 2 is a divisor of 8240)
  • 8240 / 3 = 2746.6666666667 (the remainder is 2, so 3 is not a divisor of 8240)
  • ...
  • 8240 / 8239 = 1.0001213739531 (the remainder is 1, so 8239 is not a divisor of 8240)
  • 8240 / 8240 = 1 (the remainder is 0, so 8240 is a divisor of 8240)

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 8240 (i.e. 90.774445743282). 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 )

  • 8240 / 1 = 8240 (the remainder is 0, so 1 and 8240 are divisors of 8240)
  • 8240 / 2 = 4120 (the remainder is 0, so 2 and 4120 are divisors of 8240)
  • 8240 / 3 = 2746.6666666667 (the remainder is 2, so 3 is not a divisor of 8240)
  • ...
  • 8240 / 89 = 92.584269662921 (the remainder is 52, so 89 is not a divisor of 8240)
  • 8240 / 90 = 91.555555555556 (the remainder is 50, so 90 is not a divisor of 8240)