Prime numbers
Prime numbers are introduced in Grade 4 Saxon Math Intermediate 4 (Chapter 6). A prime number is a counting number with exactly two different factors: itself and 1. The number 1 is not prime because it has only one factor. The smallest primes are 2, 3, 5, 7, 11, 13. To check if a number is prime, test whether it can be divided evenly by any number other than 1 and itself — 13 is prime because no number from 2 through 6 divides it evenly.
Key Concepts
Property 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.
Example The number 7 is prime because its only factors are 1 and 7, as shown by $1 \times 7 = 7$. 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.
Explanation 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 $1 \times 7$ or $1 \times 11$. They are the basic building blocks for all other numbers.
Common Questions
What makes a number prime?
A prime number has exactly two different factors: 1 and itself. For example, 7 is prime because only 1 x 7 = 7. No other whole number multiplication gives 7.
Is the number 1 a prime number?
No. 1 has only one factor (itself), not two different factors. A prime number must have exactly two distinct factors: 1 and itself.
How do you check if 13 is prime?
Test division by 2, 3, 4, 5, 6 (all numbers up to the square root of 13). None divide 13 evenly, so 13 is prime.
What are the prime numbers less than 20?
2, 3, 5, 7, 11, 13, 17, 19. Note that 2 is the only even prime. All other even numbers have 2 as a factor in addition to 1 and themselves, making them composite.
What is the difference between a prime number and a multiple?
A prime has exactly two factors (1 and itself). A multiple is a number you reach by skip-counting: multiples of 5 are 5, 10, 15, 20. These are different concepts — multiples of 6 include composite numbers like 12.