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### Course: Pre-algebra>Unit 1

Lesson 2: Prime and composite numbers

# Prime and composite numbers intro

Learn about prime and composite numbers and practice identifying them.

## Let's review factors

Factors are whole numbers that can be divided evenly into another number.
$1,3,5,$ and $15$ are factors of $15$ because they can all be divided into $15$ without a remainder.
$15÷1=15$
$15÷3=5$
$15÷5=3$
$15÷15=1$
$15$ has four factors: $1,3,5$, and $15$.
Problem 1A
Which of the following numbers are factors of $17$?

All numbers have $1$ and $\text{themselves}$ as factors.
$3÷1=3$
$3÷3=1$

## Categories of numbers

We can divide almost all numbers into two categories: prime numbers and composite numbers.

### Prime numbers

Prime numbers are numbers with exactly $2$ factors.
A prime number's only factors are $1$ and the number $\text{itself}$.
$7$ is an example of a prime number. Its only factors are $1$ and $7$. It is not evenly divisible by any other whole numbers.
Let's use pictures to visualize prime numbers.
Farmer Maxwell is making a chicken coop for his best egg laying hens. He has $7$ hens and is thinking about how he can arrange them. He wants to arrange the hens in equal sized groups.
The only possibility is to make $1$ row of $7$ hens.
Any other arrangements would not have the same number of hens in each row.
When there is only one possible way to divide a number into equal sized groups, that number is prime.
Problem 2A
Is $13$ a prime number?

## Composite numbers

Composite numbers have more than $2$ factors.
$16$ is an example of a composite number. The factors of $16$ are $1,2,4,8$ and $16.$ All of these numbers divide into $16$ evenly.
Let's use pictures to visualize composite numbers.
Farmer Maxwell is also inventing a new egg carton where he will store the eggs his hens lay. He wants each carton to hold $16$ eggs.
He could have $1$ row of $16$ eggs.
He could also have $2$ rows with $8$ eggs in each row.
Or he could have $4$ rows with $4$ eggs in each row.
Composite numbers have more than one way that they can be divided into equal groups.
Problem 3A
Is $15$ a composite number?

### The number $1$‍

$1$ does not fit into either category. It is neither prime nor composite.

## Practice with prime and composite numbers

Problem 4A
The numbers $11,17,$ and $23$ are all
numbers.

## Prime number and composite number challenge

Use the clues given to solve the problems below.
Problem 5A
Identify a prime number with $5$ in the ones place.

## Want to join the conversation?

• Is 0 an even number or an odd
• Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. ... Not only is 0 divisible by 2, it is divisible by every power of 2, which is relevant to the binary numeral system used by computers. In this sense, 0 is the "most even" number of all.
• Why is one not prime nor composite? What is it called?
• 1 is not composite because 1 does not have more than 2 factors, and all composite numbers have more than 2 factors.

1 is not prime because prime numbers are divisible by 1 and the number itself. 1 only contains itself and no other number. 1 belongs to its own unique category named "units."
• Is every even number a composite number because every even number has a factor of 2 except for 0 and 2.
• Yes, all even numbers except 2 and zero are composite numbers.
Zero is neither prime nor composite.
• Can all prime numbers be odd?
• 2 is the only even prime number because every other even number is divisible by 2. All other prime numbers are odd.
• This is fun
• why is math called math?
• The word mathematics comes from Ancient Greek máthēma (μάθημα), meaning "that which is learnt", "what one gets to know", hence also "study" and "science". The word came to have the narrower and more technical meaning of "mathematical study" even in Classical times.-wikapieda
• Two is a prime number because prime numbers only have two factors,right?
• yes you are correct