8/12/2023 0 Comments Prime factors numbers list![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis Use the information below to generate a citation. Then you must include on every digital page view the following attribution: ![]() If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, ![]() Want to cite, share, or modify this book? This book uses the We generally write the prime factorization in order from least to greatest. The prime factorization is the product of the circled primes. The factor 4 4 is composite, and it factors into 2 The factor 3 3 is prime, so we circle it. We write these factors on the tree under the 12. The factor 12 12 is composite, so we need to find its factors. We write 3 3 and 12 12 below 36 36 with branches connecting them. We can start with any factor pair such as 3 3 and 12. When the factor tree is complete, the circled primes give us the prime factorization.įor example, let’s find the prime factorization of 36. ![]() We continue until all the branches end with a prime. If a factor is not prime, we repeat this process, writing it as the product of two factors and adding new branches to the tree. If a factor is prime, we circle it (like a bud on a tree), and do not factor that “branch” any further. We write the factors below the number and connect them to the number with a small line segment-a “branch” of the factor tree. We start by writing the number, and then writing it as the product of two factors. One way to find the prime factorization of a number is to make a factor tree. (As you might imagine, this method is designed for smaller numbers. So be sure to check the quotient every time before proceeding. write the prime factorization of n in base 10 and concatenate the factors iterate until a prime is reached. If we didn't notice that 701 was a prime, we'd have gone on to check 5, 7, 11, 13, and so on, going through 120 more primes before getting done. This is a list of articles about prime numbers. Add 701 to the list of prime factors, and we're done. The table of prime numbers will tell you that 701 is a prime. It doesn't divide cleanly, so we go to the next prime number.Ģ103 ÷ 3 is 701, with no remainder. The next example illustrates why: Example: Prime factors of 2103Ģ103 ÷ 2 is 1051.5. The prime factors of 700 are 2 x 2 x 5 x 5 x 7.īe sure to check at each step to see if the number you have is a prime. Add 7 to the list of prime factors, and we're done. Add 5 to the list of prime factors.ħ is a prime number. Add 5 to the list of prime factors.ģ5 ÷ 5 = 7, with no remainder. It doesn't divide cleanly, so we go to the next prime number.ġ75 ÷ 5 = 35, with no remainder. It doesn't divide cleanly, so we go to the next prime number.ġ75 ÷ 3 = 58.33. Add 2 to the list of prime factors.ġ75 ÷ 2 = 87.5. Add 2 to the list of prime factors.ģ50 ÷ 2 = 175, with no remainder. If it does not divide cleanly, return to step 2, but move on to the next prime on the list.ħ00 ÷ 2 = 350, with no remainder.Take the quotient as your new number to work with, and return to step 1. If it divides cleanly, with no remainder, then add that prime to the list of prime factors.If it's not prime, try dividing it by a prime number, starting with 2.If it is prime, add it to the list of prime factors, and you're done. If it's below 1000, use the table of prime numbers. To find the prime factors of a given number, follow these steps: Examples:ġ0 is the product of the prime factors 2 x 5ġ2 is the product of the prime factors 2 x 2 x 3ģ24 is the product of the prime factors 2 x 2 x 3 x 3 x 3 x 3ħ00 is the product of the prime factors 2 x 2 x 5 x 5 x 7Ģ103 is the product of the prime factors 3 x 701 Factors that are prime numbers are called prime factors.Įvery whole number greater than one is either a prime number, or can be described as a product of prime factors. ![]() Some numbers can be evenly divided only by 1 and themselves. ![]()
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