Factors
Prime numbers are whole numbers greater than 1 with exactly two factors: 1 and themselves. In Grade 6 Saxon Math Course 1, students distinguish primes (2, 3, 5, 7, 11…) from composite numbers (which have more than two factors) and recognize that 1 is neither prime nor composite. Testing whether 51 is prime requires checking divisibility by all primes up to √51 ≈ 7.1: since 51 = 3 × 17, it is composite. Identifying primes is foundational to prime factorization and GCF/LCM computations.
Key Concepts
Contextual Explanation Prime numbers are the VIPs of math because they have exactly two factors: 1 and themselves. They can't be divided evenly by anything else! This 'unbreakable' quality makes them fundamental building blocks for all other numbers. The number 1 is not prime because it only has one lonely factor. Full Example Problem : The first four prime numbers are 2, 3, 5, and 7. What are the next four prime numbers? Solution : We check the numbers after 7 and eliminate any that aren't prime. List numbers : $8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19$. Cross out evens (divisible by 2): $9, 11, 13, 15, 17, 19$. Cross out multiples of 3 : 9 and 15 are out. The numbers left are 11, 13, 17, and 19 .
Common Questions
What makes a number prime?
A prime number has exactly two factors: 1 and the number itself.
Is 51 a prime or composite number?
Composite. 51 = 3 × 17, so it has factors other than 1 and 51.
Why is 1 not a prime number?
A prime must have exactly two distinct factors. The number 1 has only one factor (itself), so it fails the definition.
What is the only even prime number?
2. Every other even number is divisible by 2, giving it at least three factors.
How can you quickly test if a number is prime?
Check divisibility by all primes up to the square root of the number. If none divide evenly, the number is prime.