What are the divisors of 2703?
1, 3, 17, 51, 53, 159, 901, 2703
- There is a total of 8 positive divisors.
- The sum of these divisors is 3888.
- The arithmetic mean is 486.
8 odd divisors
1, 3, 17, 51, 53, 159, 901, 2703
How to compute the divisors of 2703?
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 2703 by each of the numbers from 1 to 2703 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 2703 / 1 = 2703 (the remainder is 0, so 1 is a divisor of 2703)
- 2703 / 2 = 1351.5 (the remainder is 1, so 2 is not a divisor of 2703)
- 2703 / 3 = 901 (the remainder is 0, so 3 is a divisor of 2703)
- ...
- 2703 / 2702 = 1.000370096225 (the remainder is 1, so 2702 is not a divisor of 2703)
- 2703 / 2703 = 1 (the remainder is 0, so 2703 is a divisor of 2703)
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 2703 (i.e. 51.990383726224). 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 )
- 2703 / 1 = 2703 (the remainder is 0, so 1 and 2703 are divisors of 2703)
- 2703 / 2 = 1351.5 (the remainder is 1, so 2 is not a divisor of 2703)
- 2703 / 3 = 901 (the remainder is 0, so 3 and 901 are divisors of 2703)
- ...
- 2703 / 50 = 54.06 (the remainder is 3, so 50 is not a divisor of 2703)
- 2703 / 51 = 53 (the remainder is 0, so 51 and 53 are divisors of 2703)