What are the divisors of 4213?
1, 11, 383, 4213
- There is a total of 4 positive divisors.
- The sum of these divisors is 4608.
- The arithmetic mean is 1152.
4 odd divisors
1, 11, 383, 4213
How to compute the divisors of 4213?
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 4213 by each of the numbers from 1 to 4213 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 4213 / 1 = 4213 (the remainder is 0, so 1 is a divisor of 4213)
- 4213 / 2 = 2106.5 (the remainder is 1, so 2 is not a divisor of 4213)
- 4213 / 3 = 1404.3333333333 (the remainder is 1, so 3 is not a divisor of 4213)
- ...
- 4213 / 4212 = 1.0002374169041 (the remainder is 1, so 4212 is not a divisor of 4213)
- 4213 / 4213 = 1 (the remainder is 0, so 4213 is a divisor of 4213)
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 4213 (i.e. 64.907626670523). 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 )
- 4213 / 1 = 4213 (the remainder is 0, so 1 and 4213 are divisors of 4213)
- 4213 / 2 = 2106.5 (the remainder is 1, so 2 is not a divisor of 4213)
- 4213 / 3 = 1404.3333333333 (the remainder is 1, so 3 is not a divisor of 4213)
- ...
- 4213 / 63 = 66.873015873016 (the remainder is 55, so 63 is not a divisor of 4213)
- 4213 / 64 = 65.828125 (the remainder is 53, so 64 is not a divisor of 4213)