What are the divisors of 1595?
1, 5, 11, 29, 55, 145, 319, 1595
- There is a total of 8 positive divisors.
- The sum of these divisors is 2160.
- The arithmetic mean is 270.
8 odd divisors
1, 5, 11, 29, 55, 145, 319, 1595
How to compute the divisors of 1595?
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 1595 by each of the numbers from 1 to 1595 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 1595 / 1 = 1595 (the remainder is 0, so 1 is a divisor of 1595)
- 1595 / 2 = 797.5 (the remainder is 1, so 2 is not a divisor of 1595)
- 1595 / 3 = 531.66666666667 (the remainder is 2, so 3 is not a divisor of 1595)
- ...
- 1595 / 1594 = 1.0006273525721 (the remainder is 1, so 1594 is not a divisor of 1595)
- 1595 / 1595 = 1 (the remainder is 0, so 1595 is a divisor of 1595)
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 1595 (i.e. 39.937451095432). 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 )
- 1595 / 1 = 1595 (the remainder is 0, so 1 and 1595 are divisors of 1595)
- 1595 / 2 = 797.5 (the remainder is 1, so 2 is not a divisor of 1595)
- 1595 / 3 = 531.66666666667 (the remainder is 2, so 3 is not a divisor of 1595)
- ...
- 1595 / 38 = 41.973684210526 (the remainder is 37, so 38 is not a divisor of 1595)
- 1595 / 39 = 40.897435897436 (the remainder is 35, so 39 is not a divisor of 1595)