What are the divisors of 5291?
1, 11, 13, 37, 143, 407, 481, 5291
- There is a total of 8 positive divisors.
- The sum of these divisors is 6384.
- The arithmetic mean is 798.
8 odd divisors
1, 11, 13, 37, 143, 407, 481, 5291
How to compute the divisors of 5291?
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 5291 by each of the numbers from 1 to 5291 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 5291 / 1 = 5291 (the remainder is 0, so 1 is a divisor of 5291)
- 5291 / 2 = 2645.5 (the remainder is 1, so 2 is not a divisor of 5291)
- 5291 / 3 = 1763.6666666667 (the remainder is 2, so 3 is not a divisor of 5291)
- ...
- 5291 / 5290 = 1.0001890359168 (the remainder is 1, so 5290 is not a divisor of 5291)
- 5291 / 5291 = 1 (the remainder is 0, so 5291 is a divisor of 5291)
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 5291 (i.e. 72.739260375673). 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 )
- 5291 / 1 = 5291 (the remainder is 0, so 1 and 5291 are divisors of 5291)
- 5291 / 2 = 2645.5 (the remainder is 1, so 2 is not a divisor of 5291)
- 5291 / 3 = 1763.6666666667 (the remainder is 2, so 3 is not a divisor of 5291)
- ...
- 5291 / 71 = 74.521126760563 (the remainder is 37, so 71 is not a divisor of 5291)
- 5291 / 72 = 73.486111111111 (the remainder is 35, so 72 is not a divisor of 5291)