In Grade 6 Saxon Math Course 1, Lesson 19 introduces students to factors and prime numbers as part of Chapter 2 on problem solving with numbers and operations. Students learn to identify factors as whole numbers that divide a given number without a remainder, and practice finding all factor pairs for numbers such as 6, 10, and 12. The lesson also uses rectangular tile arrays as a visual model to connect divisibility to factor pairs.
Section 1
📘 Factors and Prime Numbers
The factors of a given number are the whole numbers that divide the given number without a remainder. Counting numbers that have exactly two factors are prime numbers.
This is your introduction to these key number properties. Now, we'll apply these definitions with worked examples on listing factors and identifying various prime numbers.
Section 2
Factors
Factors are the building blocks you multiply to get another number, like ingredients in a recipe! If you can divide a number by another with zero leftovers, you've found a factor. This trick helps break down big numbers into simple parts, making them much easier to work with.
Problem: What are the factors of 14?
Solution: The factors of 14 are all numbers that divide 14 with no remainder. We can find them by testing division or finding multiplication pairs.
These divisions show the factors are 1, 2, 7, and 14. This can also be shown with a 1-by-14 rectangle and a 2-by-7 rectangle.
Section 3
Prime numbers
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.
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.
Section 4
The Prime Number Sieve
Finding primes one by one is slow. The Sieve method is a genius shortcut where you get rid of all the numbers that aren't prime. It’s like panning for gold—you wash away the dirt (multiples of 2, 3, 5, etc.) to find the valuable gold nuggets (the prime numbers) that remain.
Problem: Use the sieve method to find all prime numbers up to 20.
Solution:
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Section 1
📘 Factors and Prime Numbers
The factors of a given number are the whole numbers that divide the given number without a remainder. Counting numbers that have exactly two factors are prime numbers.
This is your introduction to these key number properties. Now, we'll apply these definitions with worked examples on listing factors and identifying various prime numbers.
Section 2
Factors
Factors are the building blocks you multiply to get another number, like ingredients in a recipe! If you can divide a number by another with zero leftovers, you've found a factor. This trick helps break down big numbers into simple parts, making them much easier to work with.
Problem: What are the factors of 14?
Solution: The factors of 14 are all numbers that divide 14 with no remainder. We can find them by testing division or finding multiplication pairs.
These divisions show the factors are 1, 2, 7, and 14. This can also be shown with a 1-by-14 rectangle and a 2-by-7 rectangle.
Section 3
Prime numbers
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.
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.
Section 4
The Prime Number Sieve
Finding primes one by one is slow. The Sieve method is a genius shortcut where you get rid of all the numbers that aren't prime. It’s like panning for gold—you wash away the dirt (multiples of 2, 3, 5, etc.) to find the valuable gold nuggets (the prime numbers) that remain.
Problem: Use the sieve method to find all prime numbers up to 20.
Solution:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter