What are the divisors of 2468?
1, 2, 4, 617, 1234, 2468
- There is a total of 6 positive divisors.
- The sum of these divisors is 4326.
- The arithmetic mean is 721.
4 even divisors
2, 4, 1234, 2468
2 odd divisors
1, 617
How to compute the divisors of 2468?
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 2468 by each of the numbers from 1 to 2468 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 2468 / 1 = 2468 (the remainder is 0, so 1 is a divisor of 2468)
- 2468 / 2 = 1234 (the remainder is 0, so 2 is a divisor of 2468)
- 2468 / 3 = 822.66666666667 (the remainder is 2, so 3 is not a divisor of 2468)
- ...
- 2468 / 2467 = 1.0004053506283 (the remainder is 1, so 2467 is not a divisor of 2468)
- 2468 / 2468 = 1 (the remainder is 0, so 2468 is a divisor of 2468)
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 2468 (i.e. 49.678969393497). 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 )
- 2468 / 1 = 2468 (the remainder is 0, so 1 and 2468 are divisors of 2468)
- 2468 / 2 = 1234 (the remainder is 0, so 2 and 1234 are divisors of 2468)
- 2468 / 3 = 822.66666666667 (the remainder is 2, so 3 is not a divisor of 2468)
- ...
- 2468 / 48 = 51.416666666667 (the remainder is 20, so 48 is not a divisor of 2468)
- 2468 / 49 = 50.367346938776 (the remainder is 18, so 49 is not a divisor of 2468)