Math Stuff: Vocabulary & Methods 1.1

Grade8Math

MATH: 1.1 Identifying Prime and Composite Numbers


- What is a Prime Number?
A number that is divided evenly to only 'two' *factors, 1 & itself.


Ex. 
3 is a prime number since you cannot divide it evenly into any number except 1 and itself (3).


- What is a Composite Number?
A number that can be divided evenly to 'more than' two factors.

Ex. 
6 is a composite number since you can divide it evenly by numbers other than 1 and itself.

6 = 1 x 6

6 = 2 x 3

6 can be divided evenly to 2 or 3 thus, it's factors are: 1, 2, 3 & 6. It has more than 2 factors so it is a composite number.

Note: 
- A prime or composite number is always a *whole number.
- Any whole number greater than 1 is either prime or composite.
- 1(one) is neither prime nor composite.
- There are no other consecutive prime numbers other than 2 and 3  because the next consecutive ones are all even numbers which is divisible by 2.
Ex. 
O - 2 & 3 (both are prime) 
X - 4 & 5 (4's divisible by 2) 
X - 6 & 7 (6's divisible by 2)
- Use the divisibility rule* to easily determine whether a number is prime or composite.

Glossary of 1.1:

*factor = the number you multiply together in a multiplication operation to get another number. (ex. 2 x 6 = 12, 2 and 6 are factors of 12)

*whole numbers = numbers 0, 1, 2, 3, 4, 5, 6 ... (& so on)
    - No decimals or fractions.
    - No negative numbers. (negative whole numbers are called integers.)

*divisibility rule = rules to test if one number is divisible by another without calculation.
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Here's a list of prime and composite numbers: (prime numbers are highlighted)

Prime and Composite Numbers

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Sample Questions:

Sample A - Identify each number as prime or composite. If the number is composite, list all of its factors.

a) 17                                      b) 25

c) 47                                      d) 48
Ans:
a) 17 (prime)
b) 25 (composite) : 1, 5 & 25
c) 47 (prime)
d) 48 (composite) : 1, 2, 3, 4, 6, 8, 12, 16, 24 & 48

Sample B - If you add a prime number to itself, is the sum composite or prime? Explain your reasoning.
Ans: 
The sum is composite. Adding a number to itself is the same thing as multiplying the number by two, making two a factor of the resulting number. Thus, it cannot be prime since it will have more than 2 factors.
Ex. 
2(prime) + 2(prime) = 2 x 2 = 4(composite)
4: 1, 2, 4 (more than 2 factors = composite)

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