for(i=2; n>1; i++)
{
while(n%i == 0)
{
printf("%d ", i);
n = n/i;
}
}
// Input: 30
// Output: 2 3 5
The given code describes an algorithm to find and print the prime factors of a given positive integer 'n'. Here's a step-by-step explanation of the code:
1. The code starts with initializing a variable 'i' to 2. This variable will be used to iterate through all potential factors of the given number 'n'.
2. The loop continues as long as 'n' is greater than 1. This is because once all prime factors have been found and divided out of 'n', it will eventually become 1, and the loop will terminate.
3. Inside the loop, there is a nested 'while' loop that continues as long as 'n' is divisible by the current value of 'i'. This is to find all occurrences of the prime factor 'i' in 'n'.
4. When 'n' is divisible by 'i', it means 'i' is a prime factor of 'n'. So, the code prints the value of 'i' using the 'printf' function.
5. After printing the prime factor 'i', the code divides 'n' by 'i', effectively reducing 'n' to the next smaller value, which still contains other prime factors.
6. The outer loop then increments 'i' to check for the next potential prime factor.
In the given example:
// Input: n = 30
The code would execute as follows:
- i = 2, n = 30: 30 is not divisible by 2.
- i = 3, n = 30: 30 is divisible by 3, so it prints 3 and updates n to 30/3 = 10.
- i = 3, n = 10: 10 is not divisible by 3.
- i = 4, n = 10: 10 is not divisible by 4.
- i = 5, n = 10: 10 is divisible by 5, so it prints 5 and updates n to 10/5 = 2.
- i = 6, n = 2: 2 is not divisible by 6.
Since the loop condition 'n>1' becomes false when 'n' is equal to 1, the loop terminates, and the prime factors of 30, which are 2, 3, and 5, are successfully printed as the output.
