Mathematical Algorithms | Prime Factorization and Divisors
Mathematically, divisor is defined as a number that divides another number completely or with a remainder.
For example: Consider 6 / 3. Here 3 divides 6 completely. Also, consider 8 /3. Here 3 does not divide 8 completely. But in both cases, 3 is the divisor.
Prime factorization is a very common topic of mathematics and is frequently used in several algorithms to solve problems. Prime factorization of a number is the process of finding which prime numbers multiply together to form the original number.
Mathematically, any number N can be expressed as:
N = p1e1 * p2e2 * p3e3 * . . . where p1, p2, p3 are prime numbers and e1, e2, e3 are the exponents of the prime numbers.
Finding these primes for any number N is called prime factorization.
Some practice problems on Prime Factorization and Divisors:
- Prime factors
- Fermat’s Last Theorem
- Sphenic Number
- Hoax Number
- Blum Integer
- Superperfect Number
- Deficient Number
- k-Rough Number or k-Jagged Number
- Perfect Number
- Aliquot sum
- Find all factors of a Natural Number
- Sum of all the factors of a number
- Total number of divisors for a given number
- Check if count of divisors is even or odd
- Frugal Number
- Betrothed numbers
- Lemoine’s Conjecture
- k-th prime factor of a given number
- Prime Factorization using Sieve O(log n) for multiple queries
- Finding power of prime number p in n!
- Program for Mobius Function
- Ordered Prime Signature
- Fast inverse square root
- Maximum number of unique prime factors
- Common Divisors of Two Numbers
- Find largest prime factor of a number
- Find if n can be written as product of k numbers
- Product of unique prime factors of a number
- Check whether a number has exactly three distinct factors or not
- Determine whether a given number is a Hyperperfect Number
- Smith Numbers
- Find numbers with n-divisors in a given range
- Pollard’s Rho Algorithm for Prime Factorization
- P-Smooth Numbers or P-friable Number
- Find sum of divisors of all the divisors of a natural number
- No of Factors of n!
- Print all prime factors and their powers
- Generation of n numbers with given set of factors
- Efficient program to print the number of factors of n numbers
- Ways to express a number as product of two different factors
- Sum of all divisors from 1 to n
- Prime factors of a big number
- Count Divisors of n in O(n^1/3)
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