What are the divisors of 5536?
1, 2, 4, 8, 16, 32, 173, 346, 692, 1384, 2768, 5536
- There is a total of 12 positive divisors.
- The sum of these divisors is 10962.
- The arithmetic mean is 913.5.
10 even divisors
2, 4, 8, 16, 32, 346, 692, 1384, 2768, 5536
2 odd divisors
1, 173
How to compute the divisors of 5536?
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 5536 by each of the numbers from 1 to 5536 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 5536 / 1 = 5536 (the remainder is 0, so 1 is a divisor of 5536)
- 5536 / 2 = 2768 (the remainder is 0, so 2 is a divisor of 5536)
- 5536 / 3 = 1845.3333333333 (the remainder is 1, so 3 is not a divisor of 5536)
- ...
- 5536 / 5535 = 1.0001806684734 (the remainder is 1, so 5535 is not a divisor of 5536)
- 5536 / 5536 = 1 (the remainder is 0, so 5536 is a divisor of 5536)
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 5536 (i.e. 74.404300950953). 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 )
- 5536 / 1 = 5536 (the remainder is 0, so 1 and 5536 are divisors of 5536)
- 5536 / 2 = 2768 (the remainder is 0, so 2 and 2768 are divisors of 5536)
- 5536 / 3 = 1845.3333333333 (the remainder is 1, so 3 is not a divisor of 5536)
- ...
- 5536 / 73 = 75.835616438356 (the remainder is 61, so 73 is not a divisor of 5536)
- 5536 / 74 = 74.810810810811 (the remainder is 60, so 74 is not a divisor of 5536)