Example 1
\(60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5\)
Alkulukuhajotelma-laskin
Etsi minkä tahansa luvun alkulukuhajotelma. Näyttää kaikki alkulukutekijät, tekijäpuut ja kompaktin eksponenttimuodon yksityiskohtaisilla vaiheilla
Tulokset
Syötä arvot ja klikkaa Laske nähdäksesi tuloksen.
Prime Factorization
Prime factorization is the process of breaking down a composite number into its prime factors. Every integer greater than 1 is either prime or can be uniquely expressed as a product of primes.
Key Concepts:
- Prime Number: A number greater than 1 with exactly two factors: 1 and itself
- Composite Number: A number with more than two factors
- Fundamental Theorem of Arithmetic: Every integer > 1 has a unique prime factorization
- Factor Tree Method: Repeatedly divide by smallest prime factors
Applications:
- Finding GCD and LCM of numbers
- Simplifying fractions and radicals
- Cryptography (RSA encryption)
- Number theory and mathematics research
Method:
- Divide the number by the smallest prime (2, 3, 5, 7, ...)
- Continue dividing the result by primes
- Stop when you reach 1
- List all prime divisors used
Worked Examples
Example 2
\(144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 = 2^4 \times 3^2\)
Example 3
\(17 \text{ is prime, so } 17 = 17\)