What are the divisors of 5542?
1, 2, 17, 34, 163, 326, 2771, 5542
- There is a total of 8 positive divisors.
- The sum of these divisors is 8856.
- The arithmetic mean is 1107.
4 even divisors
2, 34, 326, 5542
4 odd divisors
1, 17, 163, 2771
How to compute the divisors of 5542?
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 5542 by each of the numbers from 1 to 5542 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 5542 / 1 = 5542 (the remainder is 0, so 1 is a divisor of 5542)
- 5542 / 2 = 2771 (the remainder is 0, so 2 is a divisor of 5542)
- 5542 / 3 = 1847.3333333333 (the remainder is 1, so 3 is not a divisor of 5542)
- ...
- 5542 / 5541 = 1.0001804728388 (the remainder is 1, so 5541 is not a divisor of 5542)
- 5542 / 5542 = 1 (the remainder is 0, so 5542 is a divisor of 5542)
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 5542 (i.e. 74.444610281739). 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 )
- 5542 / 1 = 5542 (the remainder is 0, so 1 and 5542 are divisors of 5542)
- 5542 / 2 = 2771 (the remainder is 0, so 2 and 2771 are divisors of 5542)
- 5542 / 3 = 1847.3333333333 (the remainder is 1, so 3 is not a divisor of 5542)
- ...
- 5542 / 73 = 75.917808219178 (the remainder is 67, so 73 is not a divisor of 5542)
- 5542 / 74 = 74.891891891892 (the remainder is 66, so 74 is not a divisor of 5542)