Factors
Factors are the whole numbers that divide evenly into a given number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these divides 12 without leaving a remainder. Every number has at least two factors — 1 and itself. Finding all factors of a number is called factoring. This is a foundational 7th grade math skill covered in Saxon Math, Course 2, and is essential for simplifying fractions, finding the GCF and LCM, and working with prime factorization.
Key Concepts
Property The factors of a number are the whole numbers that divide the number without a remainder.
Examples The factors of 20 are 1, 2, 4, 5, 10, and 20. The factor pairs of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). The factors of 23 are just 1 and 23, making it a prime number.
Explanation Think of factors as a number's secret building blocks! They are the whole numbers you can multiply together to create that number. This also means they can divide the number perfectly, leaving no messy leftovers or remainders. Finding them is like a treasure hunt for all the multiplication pairs that build your number!
Common Questions
What are factors in math?
Factors are whole numbers that divide another number evenly (with no remainder). The factors of 12 are 1, 2, 3, 4, 6, and 12.
How do you find all the factors of a number?
Start with 1 and the number itself, then test each whole number in between. If it divides evenly, it’s a factor. For 18: 1, 2, 3, 6, 9, 18 are all factors; 4, 5, 7, 8 are not.
What is the difference between factors and multiples?
Factors are numbers that divide into a given number evenly. Multiples are the products when you multiply a number by 1, 2, 3, etc. For 4: factors of 12 include 4; multiples of 4 are 4, 8, 12, 16...
What is a factor pair?
A factor pair is two numbers that multiply together to give the original number. The factor pairs of 12 are: (1, 12), (2, 6), and (3, 4).
How do factors relate to the GCF?
The Greatest Common Factor (GCF) is the largest number that appears in the factor lists of two or more numbers. Finding all factors is the first step in calculating the GCF.
When do students learn about factors?
Factors are introduced in elementary school and extended in 7th grade to connect with prime factorization, GCF, and fraction simplification.
Which textbook covers factors?
Saxon Math, Course 2 covers factors and how to find them.