What are the divisors of 5534?
1, 2, 2767, 5534
- There is a total of 4 positive divisors.
- The sum of these divisors is 8304.
- The arithmetic mean is 2076.
2 even divisors
2, 5534
2 odd divisors
1, 2767
How to compute the divisors of 5534?
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 5534 by each of the numbers from 1 to 5534 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 5534 / 1 = 5534 (the remainder is 0, so 1 is a divisor of 5534)
- 5534 / 2 = 2767 (the remainder is 0, so 2 is a divisor of 5534)
- 5534 / 3 = 1844.6666666667 (the remainder is 2, so 3 is not a divisor of 5534)
- ...
- 5534 / 5533 = 1.0001807337791 (the remainder is 1, so 5533 is not a divisor of 5534)
- 5534 / 5534 = 1 (the remainder is 0, so 5534 is a divisor of 5534)
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 5534 (i.e. 74.390859653589). 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 )
- 5534 / 1 = 5534 (the remainder is 0, so 1 and 5534 are divisors of 5534)
- 5534 / 2 = 2767 (the remainder is 0, so 2 and 2767 are divisors of 5534)
- 5534 / 3 = 1844.6666666667 (the remainder is 2, so 3 is not a divisor of 5534)
- ...
- 5534 / 73 = 75.808219178082 (the remainder is 59, so 73 is not a divisor of 5534)
- 5534 / 74 = 74.783783783784 (the remainder is 58, so 74 is not a divisor of 5534)