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We cover how to find the prime factorization of a number and briefly mention a few areas where doing this may come in handy. One of the basic concepts of mathematics is expressing numbers in terms of smaller numbers, whether by addition seven is the sum of three and four , multiplication 12 is the product of three and four , or exponentiation 81 is three to the fourth power.
We often find it useful to break a number down into smaller numbers. Given a number, we call any number that divides evenly into it one of its factors , where dividing evenly means there is no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12, because 12 can be divided by each of these with no remainder.
So what is prime factorization? Recall that a prime number is any whole number that is, a positive integer that can only be divided by itself and one; every whole number that is not prime is composite , with the exception of one itself, which is neither prime nor composite.
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?
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MooMooMath provides Math help videos,step by step Math help,math equations,infographics, math calculators and more · Hello Scholars, at this point in the class instruction you have had the opportunity to review essay on eating disorders in teenage girls the material in do my homework of prime factorization the I .
Worksheet on prime factor decomposition using the factor tree method. Also includes a question on using prime factorisation and Venn diagrams to find the HCF and LCM. Ideal for a review task or homework sheet/5(13). 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.
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