What are the divisors of 3934?
1, 2, 7, 14, 281, 562, 1967, 3934
- There is a total of 8 positive divisors.
- The sum of these divisors is 6768.
- The arithmetic mean is 846.
4 even divisors
2, 14, 562, 3934
4 odd divisors
1, 7, 281, 1967
How to compute the divisors of 3934?
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 3934 by each of the numbers from 1 to 3934 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 3934 / 1 = 3934 (the remainder is 0, so 1 is a divisor of 3934)
- 3934 / 2 = 1967 (the remainder is 0, so 2 is a divisor of 3934)
- 3934 / 3 = 1311.3333333333 (the remainder is 1, so 3 is not a divisor of 3934)
- ...
- 3934 / 3933 = 1.0002542588355 (the remainder is 1, so 3933 is not a divisor of 3934)
- 3934 / 3934 = 1 (the remainder is 0, so 3934 is a divisor of 3934)
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 3934 (i.e. 62.721607122267). 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 )
- 3934 / 1 = 3934 (the remainder is 0, so 1 and 3934 are divisors of 3934)
- 3934 / 2 = 1967 (the remainder is 0, so 2 and 1967 are divisors of 3934)
- 3934 / 3 = 1311.3333333333 (the remainder is 1, so 3 is not a divisor of 3934)
- ...
- 3934 / 61 = 64.491803278689 (the remainder is 30, so 61 is not a divisor of 3934)
- 3934 / 62 = 63.451612903226 (the remainder is 28, so 62 is not a divisor of 3934)