A: The prime components are: 2 x 17 or also written together 2, 17 created in exponential form: 21 x 171

Why is the element factorization that 34 created as 21 x 171?

What is prime factorization?

Prime factorization or prime element decomposition is the process of detect which prime numbers can be multiplied together to do the initial number.

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Finding the prime components of 34

To find the element factors, you begin by separating the number by the first prime number, i m sorry is 2. If there is not a remainder, definition you can divide evenly, then 2 is a aspect of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how numerous 2"s you were able to division by evenly. Now shot dividing through the following prime factor, which is 3. The goal is to gain to a quotient that 1.


If that doesn"t make feeling yet, let"s try it...

Here room the an initial several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let"s start by dividing 34 by 2

34 ÷ 2 = 17 - No remainder! 2 is one of the factors!17 ÷ 2 = 8.5 - there is a remainder. We can"t divide by 2 evenly anymore. Let"s shot the next prime number17 ÷ 3 = 5.6667 - This has a remainder. 3 is not a factor.17 ÷ 5 = 3.4 - This has a remainder. 5 is not a factor.17 ÷ 7 = 2.4286 - This has a remainder. 7 is no a factor....Keep trying significantly larger numbers till you uncover one the divides evenly.

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...17 ÷ 17 = 1 - No remainder! 17 is among the factors!

The orange divisor(s) over are the prime factors of the number 34. If us put every one of it together we have actually the determinants 2 x 17 = 34. The can likewise be written in exponential type as 21 x 171.

Factor Tree

Another means to do prime administer is to use a variable tree. Below is a aspect tree because that the number 34.

34
*
217

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