Discover the prime factorization for 18 and understand the concept through an explanation of the method, factors exploration, and examples for practice.
Prime Factorization for 18
Definition and Explanation
Prime factorization is the process of breaking down a number into its prime factors, which are the prime numbers that multiply together to give the original number. In the case of 18, prime factorization involves finding the prime numbers that, when multiplied, equal 18.
Method of Prime Factorization
To find the prime factorization of 18, we can use a method called factorization by division. We start by dividing the number by the smallest prime number, which is 2. If the number is divisible by 2, we continue dividing until it is no longer divisible. Then, we move on to the next prime number and repeat the process until we have divided the number completely.
Factors of 18
Before we dive into the prime factorization of 18, let’s first look at the factors of 18. Factors are the numbers that can divide evenly into another number without leaving a remainder. For 18, its factors are 1, 2, 3, 6, 9, and 18.
Prime Factorization of 18
To find the prime factorization of 18, we start by dividing it by the smallest prime number, which is 2. Since 18 is divisible by 2, we divide it by 2 and get 9. Then, we continue dividing 9 by 3, another prime number, and get 3. Finally, we have divided 18 completely and obtained its prime factorization: 2 × 3 × 3.
Prime Factorization Tree for 18
A prime factorization tree is a graphical representation of the prime factors of a number. To create a prime factorization tree for 18, we start with the number and divide it by its smallest prime factor, which is 2. Then, we continue dividing each resulting quotient by the smallest prime factor until we obtain only prime numbers. The tree for 18 would look like this:
18
/ \
2 9
/ \
3 3Examples and Practice Problems
Let’s practice finding the prime factorization of 18 with a few examples:
Example 1:
Find the prime factorization of 18.
Solution:
We start by dividing 18 by 2, which gives us 9. Then, we divide 9 by 3, resulting in 3. Since 3 is a prime number, we have obtained the prime factorization of 18: 2 × 3 × 3.
Example 2:
Write the prime factorization of 18 as a product of prime numbers.
Solution:
The prime factorization of 18 is 2 × 3 × 3.
By understanding the concept of prime factorization and practicing with examples, you can easily break down numbers into their prime factors. This knowledge is useful in various mathematical fields and problem-solving scenarios.
