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## 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, comma, 3, comma, 5, comma and 15 are factors of 15 because they can all be divided into 15 without a remainder.
15, divided by, 1, equals, 15
15, divided by, 3, equals, 5
15, divided by, 5, equals, 3
15, divided by, 15, equals, 1
15 has four factors: 1, comma, 3, comma, 5, and 15.
Problem 1A
Which of the following numbers are factors of 17?

All numbers have start color #1fab54, 1, end color #1fab54 and start color #7854ab, start text, t, h, e, m, s, e, l, v, e, s, end text, end color #7854ab as factors.
3, divided by, start color #1fab54, 1, end color #1fab54, equals, 3
3, divided by, start color #7854ab, 3, end color #7854ab, equals, 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 start color #1fab54, 1, end color #1fab54 and the number start color #7854ab, start text, i, t, s, e, l, f, end text, end color #7854ab.
7 is an example of a prime number. Its only factors are start color #1fab54, 1, end color #1fab54 and 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 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.
An array of 7 hens arranged in 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, comma, 2, comma, 4, comma, 8 and 16, point 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.
An array of 16 eggs arranged in 1 row of 16 eggs.
He could also have 2 rows with 8 eggs in each row.
An array of 16 eggs arranged in 2 rows of 8 eggs each.
Or he could have 4 rows with 4 eggs in each row.
An array of 16 eggs arranged in 4 rows of 4 eggs each.
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

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

## Practice with prime and composite numbers

Problem 4A
The numbers 11, comma, 17, comma 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 prime number is created
• Two is a prime number because prime numbers only have two factors,right?
• Is this important??
• yes this is important
• 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
(1 vote)
• what was the frist prime number.
• Can all prime numbers be odd?
• are all whole numbers ending in 6 composite
• I wonder why they make composite and prime numbers?