What are the divisors of 4906?
1, 2, 11, 22, 223, 446, 2453, 4906
- There is a total of 8 positive divisors.
- The sum of these divisors is 8064.
- The arithmetic mean is 1008.
4 even divisors
2, 22, 446, 4906
4 odd divisors
1, 11, 223, 2453
How to compute the divisors of 4906?
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 4906 by each of the numbers from 1 to 4906 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 4906 / 1 = 4906 (the remainder is 0, so 1 is a divisor of 4906)
- 4906 / 2 = 2453 (the remainder is 0, so 2 is a divisor of 4906)
- 4906 / 3 = 1635.3333333333 (the remainder is 1, so 3 is not a divisor of 4906)
- ...
- 4906 / 4905 = 1.0002038735984 (the remainder is 1, so 4905 is not a divisor of 4906)
- 4906 / 4906 = 1 (the remainder is 0, so 4906 is a divisor of 4906)
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 4906 (i.e. 70.04284403135). 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 )
- 4906 / 1 = 4906 (the remainder is 0, so 1 and 4906 are divisors of 4906)
- 4906 / 2 = 2453 (the remainder is 0, so 2 and 2453 are divisors of 4906)
- 4906 / 3 = 1635.3333333333 (the remainder is 1, so 3 is not a divisor of 4906)
- ...
- 4906 / 69 = 71.101449275362 (the remainder is 7, so 69 is not a divisor of 4906)
- 4906 / 70 = 70.085714285714 (the remainder is 6, so 70 is not a divisor of 4906)