It allows you to find all the factors of a number. Prime factorisation is necessary for calculating the greatest common factor and least common multiple of sets of numbers. That information is essential for working with rational numbers.
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It can be used to simplify fractions. This can often make the numbers in a calculation smaller and so easier to deal with. Very large factors of primes are used for encrypting data for security.
Finding least common multiple, greatest common factor; simplifying square roots.
Really isn't any practical uses. It just gets you familiar with numbers and prime numbers and it gets your brain thinking.
A Venn diagram may be used to display a prime factorization.
That is not what prime factorization is for.
What is the prime factorization of 256^180
3 is already prime. No factorization.
113 is already prime. No factorization.