Given a number N, print all the prime factors and their powers. Here N <= 10^18
Input : 250 Output : 2 1 5 3 Explanation: The prime factors of 250 are 2 and 5. 2 appears once in the prime factorization of and 5 is thrice in it. Input : 1000000000000000000 Output : 2 18 5 18 Explanation: The prime factors of 1000000000000000000 are 2 and 5. The prime factor 2 appears 18 times in the prime factorization. 5 appears 18 times.
We cannot use Sieve’s implementation for a single large number as it requires proportional space. We first count the number of times 2 is the factor of the given number, then we iterate from 3 to Sqrt(n) to get the number of times a prime number divides a particular number which reduces every time by n/i. We divide our number n (whose prime factorization is to be calculated) by its corresponding smallest prime factor till n becomes 1. And if at the end n>2, it means its a prime number, so we print that particular number.
2 18 5 18
Time complexity : O(sqrt(n)).
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