Given a perfect square natural number N. The task is to find all the factors of N.
Input: N = 100
Output: 1 2 4 5 10 20 25 50 100
Input: N = 900
Output: 1 2 4 3 6 12 9 18 36 5 10 20 15 30 60 45 90 180 25 50 100 75 150 300 225 450 900
- Find the square root of N in temp.
- Find all the prime factors of temp in O(sqrt(temp)) using the approach discussed in this article.
- Initialise an array factor with element 1 in it.
- Store all the prime factors of temp obtained in above step twice in an array factor.
- Initialise a matrix M such that for every element in factor starting from index 1:
- If factor[i] is equals to factor[i-1], then store factor[i]*factor[i-1] in matrix M in row i – 1 .
- Else factor[i] is not equals to factor[i-1], then store factor[i]*factor[i-1] in matrix M in row i.
- Initialise two arrays arr1 and arr2 with the element 1 in both the array.
- Iterate over every row of matrix M such that the product of every element in arr1 with every element of current row must be stored in arr2.
- After above step, copy every element of arr2 in arr1.
- Repeat above two steps, till all the element of matrixM is traverse.
- The array arr2 contains all the factors of number N.
Below is the implementation of the above approach:
1 2 4 3 6 12 9 18 36 5 10 20 15 30 60 45 90 180 25 50 100 75 150 300 225 450 900
Time Complexity: O(sqrt(sqrt(N)))
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