Given two integer and , the task is to find the count of common factors of two numbers where factors are prime.
Input: A = 6, B = 12
2 and 3 are the only common prime divisors of 6 and 12
Input: A = 4, B = 8
Naive Approach: Iterate from 1 to min(A, B) and check whether i is prime and a factor of both A and B, if yes then increment the counter.
Efficient Approach is to do following:
Below is the implementation of the above approach:
If there are multiple queries for counting common divisors, we can further optimize above code using Prime Factorization using Sieve O(log n) for multiple queries
- Common prime factors of two numbers
- Count numbers from range whose prime factors are only 2 and 3
- Count numbers in a range having GCD of powers of prime factors equal to 1
- Print all numbers whose set of prime factors is a subset of the set of the prime factors of X
- K-Primes (Numbers with k prime factors) in a range
- Number of distinct prime factors of first n natural numbers
- Count of common multiples of two numbers in a range
- Count of numbers below N whose sum of prime divisors is K
- Find count of Almost Prime numbers from 1 to N
- Numbers in range [L, R] such that the count of their divisors is both even and prime
- Sum of numbers in a range [L, R] whose count of divisors is prime
- Count all the numbers less than 10^6 whose minimum prime factor is N
- Count Numbers in Range with difference between Sum of digits at even and odd positions as Prime
- Queries for the difference between the count of composite and prime numbers in a given range
- Absolute difference between the Product of Non-Prime numbers and Prime numbers of an Array
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