Prime and composite numbers intro

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.

$15$‍ has four factors: $1,3,5$‍, and $15$‍.

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

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

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.

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

Use the clues given to solve the problems below.