In this Grade 4 Saxon Math Intermediate 4 lesson, students learn to identify multiples and factors, then use those concepts to distinguish between prime numbers (exactly two factors: 1 and itself) and composite numbers (more than two factors). Students practice listing multiples of given numbers, finding all factors of a number using multiplication tables, and classifying numbers like 7, 9, and 11 as prime or composite. The activity also uses arrays on grid paper to help students visually discover factor pairs for numbers such as 8 and 10.
Section 1
📘 Prime and Composite Numbers
A prime number is a counting number that has exactly two different factors, itself and 1. A counting number with more than two factors is a composite number.
Next, you’ll use this definition to practice identifying prime numbers, find factors, and solve problems involving multiples.
Section 2
What are multiples
A multiple is a product of a given number and a counting number. The multiples of any counting number are the products we get when we multiply the number by 1, 2, 3, 4, 5, 6, and so on. For example, the first four multiples of 3 are 3, 6, 9, and 12.
The first four multiples of 7 are: , , , and .
The third multiple of 8 is found by calculating .
Twelve is a multiple of 1, 2, 3, 4, 6, and 12 because each of those numbers can be multiplied by another whole number to equal 12.
Think of multiples as the numbers you land on when you're skip-counting. If you start at 7 and keep adding 7, you get 14, 21, 28, and so on—these are all multiples of 7! It’s just a way of showing the results from a number’s multiplication table in a sequence that can go on forever.
Section 3
Prime numbers
A prime number is a counting number that has exactly two different factors, itself and 1. The number 1 is not a prime number because its only factor is 1. The numbers 2 and 3 are prime numbers because their only factors are 1 and themselves.
The number 7 is prime because its only factors are 1 and 7, as shown by .
The numbers 2, 3, 5, and 11 are all prime numbers because they each have exactly two factors.
To check if 13 is prime, we see it cannot be divided evenly by 2, 3, 4, 5, or 6. Thus, 13 is prime.
Prime numbers are the ultimate loners of the number world. They can't be made by multiplying any smaller whole numbers, except for 1 and themselves. Think of 7 or 11—no matter how you try, you can only get to them by doing or . They are the basic building blocks for all other numbers.
Section 4
Composite number
A counting number with more than two factors is a composite number. The number 4 is a classic example of a composite number because it has three factors: 1, 2, and 4. If a counting number greater than 1 is not prime, then it must be composite.
The number 9 is composite because it has three factors (1, 3, and 9) since and .
The number 10 is composite because it can be divided by 2 and 5, giving it the factors 1, 2, 5, and 10.
We can show 8 is composite by making a rectangle, proving it has factors other than 1 and 8.
Composite numbers are the social butterflies! Unlike primes, they have more than two factors and can be formed by multiplying different pairs of numbers. For instance, the number 12 is very composite because you can make it with or . They are 'composed' of smaller factors, which is an easy way to remember the name.
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Section 1
📘 Prime and Composite Numbers
A prime number is a counting number that has exactly two different factors, itself and 1. A counting number with more than two factors is a composite number.
Next, you’ll use this definition to practice identifying prime numbers, find factors, and solve problems involving multiples.
Section 2
What are multiples
A multiple is a product of a given number and a counting number. The multiples of any counting number are the products we get when we multiply the number by 1, 2, 3, 4, 5, 6, and so on. For example, the first four multiples of 3 are 3, 6, 9, and 12.
The first four multiples of 7 are: , , , and .
The third multiple of 8 is found by calculating .
Twelve is a multiple of 1, 2, 3, 4, 6, and 12 because each of those numbers can be multiplied by another whole number to equal 12.
Think of multiples as the numbers you land on when you're skip-counting. If you start at 7 and keep adding 7, you get 14, 21, 28, and so on—these are all multiples of 7! It’s just a way of showing the results from a number’s multiplication table in a sequence that can go on forever.
Section 3
Prime numbers
A prime number is a counting number that has exactly two different factors, itself and 1. The number 1 is not a prime number because its only factor is 1. The numbers 2 and 3 are prime numbers because their only factors are 1 and themselves.
The number 7 is prime because its only factors are 1 and 7, as shown by .
The numbers 2, 3, 5, and 11 are all prime numbers because they each have exactly two factors.
To check if 13 is prime, we see it cannot be divided evenly by 2, 3, 4, 5, or 6. Thus, 13 is prime.
Prime numbers are the ultimate loners of the number world. They can't be made by multiplying any smaller whole numbers, except for 1 and themselves. Think of 7 or 11—no matter how you try, you can only get to them by doing or . They are the basic building blocks for all other numbers.
Section 4
Composite number
A counting number with more than two factors is a composite number. The number 4 is a classic example of a composite number because it has three factors: 1, 2, and 4. If a counting number greater than 1 is not prime, then it must be composite.
The number 9 is composite because it has three factors (1, 3, and 9) since and .
The number 10 is composite because it can be divided by 2 and 5, giving it the factors 1, 2, 5, and 10.
We can show 8 is composite by making a rectangle, proving it has factors other than 1 and 8.
Composite numbers are the social butterflies! Unlike primes, they have more than two factors and can be formed by multiplying different pairs of numbers. For instance, the number 12 is very composite because you can make it with or . They are 'composed' of smaller factors, which is an easy way to remember the name.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter