What are the divisors of 331?
1, 331
- There is a total of 2 positive divisors.
- The sum of these divisors is 332.
- The arithmetic mean is 166.
2 odd divisors
1, 331
How to compute the divisors of 331?
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 331 by each of the numbers from 1 to 331 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 331 / 1 = 331 (the remainder is 0, so 1 is a divisor of 331)
- 331 / 2 = 165.5 (the remainder is 1, so 2 is not a divisor of 331)
- 331 / 3 = 110.33333333333 (the remainder is 1, so 3 is not a divisor of 331)
- ...
- 331 / 330 = 1.0030303030303 (the remainder is 1, so 330 is not a divisor of 331)
- 331 / 331 = 1 (the remainder is 0, so 331 is a divisor of 331)
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 331 (i.e. 18.19340539866). 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 )
- 331 / 1 = 331 (the remainder is 0, so 1 and 331 are divisors of 331)
- 331 / 2 = 165.5 (the remainder is 1, so 2 is not a divisor of 331)
- 331 / 3 = 110.33333333333 (the remainder is 1, so 3 is not a divisor of 331)
- ...
- 331 / 17 = 19.470588235294 (the remainder is 8, so 17 is not a divisor of 331)
- 331 / 18 = 18.388888888889 (the remainder is 7, so 18 is not a divisor of 331)