The prime factors of a number are just those factors that happen to be prime; the fundamental theorem of arithmetic states that every positive integer can be uniquely factored into a set of prime numbers, which we call the prime factorization.
Twelve is the product of three and four, three is prime, four is the product of two and two, and two is prime. How about another example? Prime factors are used frequently in advanced mathematics. For example, cryptographic software often depends on the difficulty of factoring very large numbers. Knowing how to find the prime factorization also makes it easy to do a number of other things, such as finding the greatest common factor, finding the least common multiple or simplifying roots.
Can you find the prime factorization of each of these numbers? The answers are below. What is the prime factorization of 21? We can find the prime factorization by starting with the smallest prime and dividing by it as many times as we can, then moving to the next larger prime.
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Could a prime factorization include 6 as one of the prime factors? Tell why or why not. Show Your Work 2 2 5 22 5 Solution: The prime factorization of 20 is 2 2 5. 4 5 2 2 5 Step 1: Start with two factors of 20 Step 2: If a factor is composite, find its factors. Step 3: Check that all factors are prime numbers. Problem Given Number Prime Composite Your Third Factor- If Composite Neither A 85 B C 0 D E 47 F G H 39 I 2, J 11, II. Use a factor tree. to determine the prime factorization in exponential form. starting with the smallest prime factor and ending with the largest prime. factor.