What are the divisors of 4243?
1, 4243
- There is a total of 2 positive divisors.
- The sum of these divisors is 4244.
- The arithmetic mean is 2122.
2 odd divisors
1, 4243
How to compute the divisors of 4243?
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 4243 by each of the numbers from 1 to 4243 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 4243 / 1 = 4243 (the remainder is 0, so 1 is a divisor of 4243)
- 4243 / 2 = 2121.5 (the remainder is 1, so 2 is not a divisor of 4243)
- 4243 / 3 = 1414.3333333333 (the remainder is 1, so 3 is not a divisor of 4243)
- ...
- 4243 / 4242 = 1.0002357378595 (the remainder is 1, so 4242 is not a divisor of 4243)
- 4243 / 4243 = 1 (the remainder is 0, so 4243 is a divisor of 4243)
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 4243 (i.e. 65.138314377945). 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 )
- 4243 / 1 = 4243 (the remainder is 0, so 1 and 4243 are divisors of 4243)
- 4243 / 2 = 2121.5 (the remainder is 1, so 2 is not a divisor of 4243)
- 4243 / 3 = 1414.3333333333 (the remainder is 1, so 3 is not a divisor of 4243)
- ...
- 4243 / 64 = 66.296875 (the remainder is 19, so 64 is not a divisor of 4243)
- 4243 / 65 = 65.276923076923 (the remainder is 18, so 65 is not a divisor of 4243)