What are the divisors of 1959?
1, 3, 653, 1959
- There is a total of 4 positive divisors.
- The sum of these divisors is 2616.
- The arithmetic mean is 654.
4 odd divisors
1, 3, 653, 1959
How to compute the divisors of 1959?
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 1959 by each of the numbers from 1 to 1959 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 1959 / 1 = 1959 (the remainder is 0, so 1 is a divisor of 1959)
- 1959 / 2 = 979.5 (the remainder is 1, so 2 is not a divisor of 1959)
- 1959 / 3 = 653 (the remainder is 0, so 3 is a divisor of 1959)
- ...
- 1959 / 1958 = 1.0005107252298 (the remainder is 1, so 1958 is not a divisor of 1959)
- 1959 / 1959 = 1 (the remainder is 0, so 1959 is a divisor of 1959)
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 1959 (i.e. 44.260591952661). 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 )
- 1959 / 1 = 1959 (the remainder is 0, so 1 and 1959 are divisors of 1959)
- 1959 / 2 = 979.5 (the remainder is 1, so 2 is not a divisor of 1959)
- 1959 / 3 = 653 (the remainder is 0, so 3 and 653 are divisors of 1959)
- ...
- 1959 / 43 = 45.558139534884 (the remainder is 24, so 43 is not a divisor of 1959)
- 1959 / 44 = 44.522727272727 (the remainder is 23, so 44 is not a divisor of 1959)