What are the divisors of 4994?
1, 2, 11, 22, 227, 454, 2497, 4994
- There is a total of 8 positive divisors.
- The sum of these divisors is 8208.
- The arithmetic mean is 1026.
4 even divisors
2, 22, 454, 4994
4 odd divisors
1, 11, 227, 2497
How to compute the divisors of 4994?
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 4994 by each of the numbers from 1 to 4994 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 4994 / 1 = 4994 (the remainder is 0, so 1 is a divisor of 4994)
- 4994 / 2 = 2497 (the remainder is 0, so 2 is a divisor of 4994)
- 4994 / 3 = 1664.6666666667 (the remainder is 2, so 3 is not a divisor of 4994)
- ...
- 4994 / 4993 = 1.0002002803925 (the remainder is 1, so 4993 is not a divisor of 4994)
- 4994 / 4994 = 1 (the remainder is 0, so 4994 is a divisor of 4994)
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 4994 (i.e. 70.668238976219). 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 )
- 4994 / 1 = 4994 (the remainder is 0, so 1 and 4994 are divisors of 4994)
- 4994 / 2 = 2497 (the remainder is 0, so 2 and 2497 are divisors of 4994)
- 4994 / 3 = 1664.6666666667 (the remainder is 2, so 3 is not a divisor of 4994)
- ...
- 4994 / 69 = 72.376811594203 (the remainder is 26, so 69 is not a divisor of 4994)
- 4994 / 70 = 71.342857142857 (the remainder is 24, so 70 is not a divisor of 4994)