Prime and composite numbers intro

Factors are whole numbers that can be divided evenly into another number.

$1, 3, 5,$1, comma, 3, comma, 5, comma and $15$15 are factors of $15$15 because they can all be divided into $15$15 without a remainder.

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

All numbers have $\greenD{1}$start color #1fab54, 1, end color #1fab54 and $\purpleD{\text{themselves}}$start color #7854ab, start text, t, h, e, m, s, e, l, v, e, s, end text, end color #7854ab as factors.

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

Prime numbers are numbers with exactly $2$2 factors.

A prime number's only factors are $\greenD1$start color #1fab54, 1, end color #1fab54 and the number $\purpleD{\text{itself}}$start color #7854ab, start text, i, t, s, e, l, f, end text, end color #7854ab.

$7$7 is an example of a prime number. Its only factors are $\greenD1$start color #1fab54, 1, end color #1fab54 and $\purpleD7$start color #7854ab, 7, end color #7854ab. 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$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$1 row of $7$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$2 factors.

$16$16 is an example of a composite number. The factors of $16$16 are $1, 2, 4, 8$1, comma, 2, comma, 4, comma, 8 and $16.$16, point All of these numbers divide into $16$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$16 eggs.

He could have $1$1 row of $16$16 eggs.

He could also have $2$2 rows with $8$8 eggs in each row.

Or he could have $4$4 rows with $4$4 eggs in each row.

Composite numbers have more than one way that they can be divided into equal groups.

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

Use the clues given to solve the problems below.