What are the divisors of 5269?
1, 11, 479, 5269
- There is a total of 4 positive divisors.
- The sum of these divisors is 5760.
- The arithmetic mean is 1440.
4 odd divisors
1, 11, 479, 5269
How to compute the divisors of 5269?
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 5269 by each of the numbers from 1 to 5269 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 5269 / 1 = 5269 (the remainder is 0, so 1 is a divisor of 5269)
- 5269 / 2 = 2634.5 (the remainder is 1, so 2 is not a divisor of 5269)
- 5269 / 3 = 1756.3333333333 (the remainder is 1, so 3 is not a divisor of 5269)
- ...
- 5269 / 5268 = 1.0001898253607 (the remainder is 1, so 5268 is not a divisor of 5269)
- 5269 / 5269 = 1 (the remainder is 0, so 5269 is a divisor of 5269)
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 5269 (i.e. 72.587877775838). 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 )
- 5269 / 1 = 5269 (the remainder is 0, so 1 and 5269 are divisors of 5269)
- 5269 / 2 = 2634.5 (the remainder is 1, so 2 is not a divisor of 5269)
- 5269 / 3 = 1756.3333333333 (the remainder is 1, so 3 is not a divisor of 5269)
- ...
- 5269 / 71 = 74.211267605634 (the remainder is 15, so 71 is not a divisor of 5269)
- 5269 / 72 = 73.180555555556 (the remainder is 13, so 72 is not a divisor of 5269)