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
- There is a total of 20 positive divisors.
- The sum of these divisors is 19344.
- The arithmetic mean is 967.2.
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.
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.
(where 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:
(thus, if , then )
- 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)