What are the divisors of 2380?
1, 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190, 2380
- There is a total of 24 positive divisors.
- The sum of these divisors is 6048.
- The arithmetic mean is 252.
16 even divisors
2, 4, 10, 14, 20, 28, 34, 68, 70, 140, 170, 238, 340, 476, 1190, 2380
8 odd divisors
1, 5, 7, 17, 35, 85, 119, 595
How to compute the divisors of 2380?
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 2380 by each of the numbers from 1 to 2380 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 2380 / 1 = 2380 (the remainder is 0, so 1 is a divisor of 2380)
- 2380 / 2 = 1190 (the remainder is 0, so 2 is a divisor of 2380)
- 2380 / 3 = 793.33333333333 (the remainder is 1, so 3 is not a divisor of 2380)
- ...
- 2380 / 2379 = 1.0004203446826 (the remainder is 1, so 2379 is not a divisor of 2380)
- 2380 / 2380 = 1 (the remainder is 0, so 2380 is a divisor of 2380)
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 2380 (i.e. 48.785243670602). 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 )
- 2380 / 1 = 2380 (the remainder is 0, so 1 and 2380 are divisors of 2380)
- 2380 / 2 = 1190 (the remainder is 0, so 2 and 1190 are divisors of 2380)
- 2380 / 3 = 793.33333333333 (the remainder is 1, so 3 is not a divisor of 2380)
- ...
- 2380 / 47 = 50.63829787234 (the remainder is 30, so 47 is not a divisor of 2380)
- 2380 / 48 = 49.583333333333 (the remainder is 28, so 48 is not a divisor of 2380)