What are the divisors of 2564?
1, 2, 4, 641, 1282, 2564
- There is a total of 6 positive divisors.
- The sum of these divisors is 4494.
- The arithmetic mean is 749.
4 even divisors
2, 4, 1282, 2564
2 odd divisors
1, 641
How to compute the divisors of 2564?
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 2564 by each of the numbers from 1 to 2564 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 2564 / 1 = 2564 (the remainder is 0, so 1 is a divisor of 2564)
- 2564 / 2 = 1282 (the remainder is 0, so 2 is a divisor of 2564)
- 2564 / 3 = 854.66666666667 (the remainder is 2, so 3 is not a divisor of 2564)
- ...
- 2564 / 2563 = 1.0003901677721 (the remainder is 1, so 2563 is not a divisor of 2564)
- 2564 / 2564 = 1 (the remainder is 0, so 2564 is a divisor of 2564)
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 2564 (i.e. 50.635955604689). 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 )
- 2564 / 1 = 2564 (the remainder is 0, so 1 and 2564 are divisors of 2564)
- 2564 / 2 = 1282 (the remainder is 0, so 2 and 1282 are divisors of 2564)
- 2564 / 3 = 854.66666666667 (the remainder is 2, so 3 is not a divisor of 2564)
- ...
- 2564 / 49 = 52.326530612245 (the remainder is 16, so 49 is not a divisor of 2564)
- 2564 / 50 = 51.28 (the remainder is 14, so 50 is not a divisor of 2564)