Divisors, Prime Factors and Radical of a Natural Number

A calculator, that finds every divisor, prime factor, distinct prime factor and the radical of a positive integer. Also the amount of divisors and prime factors will be counted. Divisors are those natural numbers, by which a positive integer can be divided without rest. For prime numbers, this is 1 and the number itself, other numbers have further divisors. Prime factors are those prime numbers which multiplicated with each other give the orininal number. The radical of a positive integer is the product of the distinct prime factors.

Example: the number 123456 has 28 divisors and 8 prime factors, 3 of those different. Its radical is 3858.

The decomposition of a natural number into divisors, or prime factors, is called factorization. The fundamental theorem of arithmetic states that for every natural number there exists a unique prime factorization. This is displayed here in the second line of the result.

Divisors, prime numbers, prime factors, and radicals are terms from number theory. Number theory was once considered the pinnacle of mathematics, but one that had no practical applications. This changed dramatically with the advent of cryptography in computer applications. Cryptography is the encryption of data, which is based on the existence of certain calculations that can be performed very easily in one direction, but are very complicated the other way around. This is especially true for prime factorization. Multiplying two prime factors is relatively easy, even for huge numbers, but factoring the result back into these prime factors for correspondingly large numbers involves such an enormous amount of computation that a computer cannot complete it in a reasonable amount of time. Therefore this calculator can quickly reach its limits with large numbers. If you enter 123456789, for example, you will notice a slight delay, depending on the speed of your computer which is running the program.