Prime numbers
Prime numbers are whole numbers greater than 1 with exactly two factors: 1 and themselves. In Grade 8 Saxon Math Course 3, students identify and work with prime numbers as building blocks for factorization, GCF, LCM, and fraction simplification. Recognizing primes supports number sense and algebraic reasoning.
Key Concepts
Property Prime numbers are counting numbers greater than 1 that have exactly two different counting number factors, the number itself and 1.
Examples The number 7 is prime because its only factors are 1 and 7. You can only form a $1 \times 7$ rectangle with 7 tiles. The number 13 is prime. Its only factor pair is $1 \times 13$, meaning it cannot be divided evenly by any other counting numbers. The number 2 is the only even prime number, because all other even numbers are divisible by 2, giving them an extra factor.
Explanation Think of prime numbers as the ultimate loners! If you have a prime number of tiles, like 7, you can only make one boring rectangle (a 7 by 1). They refuse to be arranged in any other interesting way because they only have two factors: themselves and 1. It’s their way or the highway, making them the basic building blocks for all other numbers.
Common Questions
What makes a number prime?
A prime number has exactly two distinct factors: 1 and itself. For example, 7 is prime because it is only divisible by 1 and 7.
How do you check if a number is prime?
Test divisibility by all primes up to the square root of the number. If none divide evenly, the number is prime.
What are the first 10 prime numbers?
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Is 2 a prime number?
Yes, 2 is the only even prime number. All other even numbers are divisible by 2 and therefore have more than two factors.
How are prime numbers used in Saxon Math Course 3?
Prime numbers are used for prime factorization, finding GCF and LCM, and simplifying fractions.