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# How you Determine if a Number is Prime.

Factor Tree

D. Russell
Prime numbers are the numbers that are bigger than one and cannot be divided evenly by any other number except 1 and itself. If a number can be divided evenly by any other number not counting itself and 1, it is not prime and is referred to as a composite number. Prime numbers are whole numbers that must be greater than 1. Zero and one are not considered prime numbers. Learn how to determine which numbers are prime. Remember, when talking about prime numbers, we are referring to whole numbers.
Difficulty: Average
Time Required: Depends on Your Grade or Previous Math Experience with Prime Numbers

### Here's How:

1. Factorization. Understand what a factor is before you start to work with prime numbers. Let's take the number 20.
Let's factor 20:
2 x 2 x 5
2 and 5 are the prime factors for 20.
This means that 20 is not a prime number.
Factors are the numbers multiplied to get the product.
We can also find more factors of 20:
5 x 4 and 2 x 10.
All the factors of 20 are: 1, 2, 4, 5, 10.

One more. Is 9 a prime number?
Let's factor 9:
3 x 3
Factors of 9 are 1, 3 and 9.
9 is not a prime number.

2. Separate Piles:
When learning about prime numbers, one of the easiest methods to start is to work with numbers in a concrete method. Use buttons, coins, dried beans etc. Start with numbers less than 100. For each number, count out that many objects.

For instance, if you want to find out if 27 is prime, begin by counting out 27 objects.
Task 1: Can 27 objects be evenly divided into 2 piles?
No
Can 27 objects be evenly divided into 3 piles?
Yes!
There are 3 piles of 9. This means that 3 and 9 are prime factors of 27. Therefore 27 is not a prime number.
Practice with objects on a variety of numbers to help understanding.

3. Calculator Method: After using the concrete method (buttons, coins etc.) and trying to separate the 17 or 23 coins evenly into 2 or 3 piles,then try the calculator method. After all, with any concept, concrete methods should be used first.

Take your calculator and key in the number you are trying to determine is prime. Let's take 57. Divide it by 2. Does it come out to an even number? No, you'll discover it's 27.5. Now divide 57 by 3. Is it even? You will see 19 which is an even number. Is 57 prime? Yes, 19 and 3 are its factors. When using the calculator to determine prime, begin by dividing it by 2 or 3 first.

4. Divisibility: Know your divisibily rules.
Try 2: Any number ending in 2 is an even number and it will be divisible by 2, therefore it is not prime.
Try 3. Take the number, and add the digits up, when those digits are divisible by 3, the number is not prime. Take 2469, those digits add up to 21, and 21 is divisible by 3, therefore 2469 is not a prime number.
Try 4. Take the last 2 digits of the number, is it divisible by 4? Then the number is divisible by 4. Try 8336, the last 2 digits are 36 which are divisible by 4, therefore 8336 is not prime.
Try 5: any number ending in 0 or 5 is divisbile by 5 and not prime.
5. Prime Number Calculator I don't recommend using the prime number calculator until the concept of prime numbers is fully understood. If that's the case, then prime number calculators are a quick and easy method to determine if a number is prime or not.
6. Prime Factorization Trees This method is similar to factorization. Take a look at the image of the factor trees. There are 3 numbers being factored: 32, 21 and 40. There is more than one way to factor numbers, however, eventually you will factor until you've reached all the common factors. For instance, if I am factoring the number 30. I could begin with 10 x 3 or 15 x 2. In each case I will continue to factor 10 (2 x 5) and I will continue to factor 15 (3 x 5) and the end resulting prime factors will be the same: 2, 3 and 5. After all, 5 x 3 x 2 = 30 as does 2 x 3 x 5.
7. Division This method is similar to the calculator method. Take your number and try to divide it by 2, if not, then try 3, if not try 4, if not try 5. This can be time consuming and not something you would want to use with very large numbers. However, for somebody starting out with prime numbers, this is a great method to help with the understanding of what makes a prime number prime.
8. Confusing for Learners:

When working with prime numbers it's important that students know the difference between factors and multiples. These two terms are easily confused by learners.

### What You Need

• Paper and Pencil
• Manipulatives: Coins, buttons, dried beans etc.
• Calculator
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Deb Russell
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