What are the divisors of 1630?
1, 2, 5, 10, 163, 326, 815, 1630
- There is a total of 8 positive divisors.
- The sum of these divisors is 2952.
- The arithmetic mean is 369.
4 even divisors
2, 10, 326, 1630
4 odd divisors
1, 5, 163, 815
How to compute the divisors of 1630?
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 1630 by each of the numbers from 1 to 1630 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 1630 / 1 = 1630 (the remainder is 0, so 1 is a divisor of 1630)
- 1630 / 2 = 815 (the remainder is 0, so 2 is a divisor of 1630)
- 1630 / 3 = 543.33333333333 (the remainder is 1, so 3 is not a divisor of 1630)
- ...
- 1630 / 1629 = 1.0006138735421 (the remainder is 1, so 1629 is not a divisor of 1630)
- 1630 / 1630 = 1 (the remainder is 0, so 1630 is a divisor of 1630)
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 1630 (i.e. 40.373258476373). 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 )
- 1630 / 1 = 1630 (the remainder is 0, so 1 and 1630 are divisors of 1630)
- 1630 / 2 = 815 (the remainder is 0, so 2 and 815 are divisors of 1630)
- 1630 / 3 = 543.33333333333 (the remainder is 1, so 3 is not a divisor of 1630)
- ...
- 1630 / 39 = 41.794871794872 (the remainder is 31, so 39 is not a divisor of 1630)
- 1630 / 40 = 40.75 (the remainder is 30, so 40 is not a divisor of 1630)