What are the divisors of 5550?
1, 2, 3, 5, 6, 10, 15, 25, 30, 37, 50, 74, 75, 111, 150, 185, 222, 370, 555, 925, 1110, 1850, 2775, 5550
- There is a total of 24 positive divisors.
- The sum of these divisors is 14136.
- The arithmetic mean is 589.
12 even divisors
2, 6, 10, 30, 50, 74, 150, 222, 370, 1110, 1850, 5550
12 odd divisors
1, 3, 5, 15, 25, 37, 75, 111, 185, 555, 925, 2775
How to compute the divisors of 5550?
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 5550 by each of the numbers from 1 to 5550 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 5550 / 1 = 5550 (the remainder is 0, so 1 is a divisor of 5550)
- 5550 / 2 = 2775 (the remainder is 0, so 2 is a divisor of 5550)
- 5550 / 3 = 1850 (the remainder is 0, so 3 is a divisor of 5550)
- ...
- 5550 / 5549 = 1.0001802126509 (the remainder is 1, so 5549 is not a divisor of 5550)
- 5550 / 5550 = 1 (the remainder is 0, so 5550 is a divisor of 5550)
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 5550 (i.e. 74.498322128757). 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 )
- 5550 / 1 = 5550 (the remainder is 0, so 1 and 5550 are divisors of 5550)
- 5550 / 2 = 2775 (the remainder is 0, so 2 and 2775 are divisors of 5550)
- 5550 / 3 = 1850 (the remainder is 0, so 3 and 1850 are divisors of 5550)
- ...
- 5550 / 73 = 76.027397260274 (the remainder is 2, so 73 is not a divisor of 5550)
- 5550 / 74 = 75 (the remainder is 0, so 74 and 75 are divisors of 5550)