Divisibility Tests
Divisibility Tests are Grade 8 number theory rules in Saxon Math Course 3, Chapter 1, that let students quickly determine if one number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 without performing full division. These mental math shortcuts are essential for simplifying fractions, finding common factors, and working with prime factorization.
Key Concepts
Property One way to test if a counting number is prime or composite is to determine if it is divisible (can be divided) by a counting number other than 1 and itself.
Examples The number 520,611 is composite because the sum of its digits is $5+2+0+6+1+1=15$, and 15 is divisible by 3. The number 1,237,526 is composite. Because it's an even number (it ends in 6), it is automatically divisible by 2. The number 3420 is divisible by 6 because it is even (divisible by 2) and the sum of its digits is 9 (divisible by 3).
Explanation Divisibility tests are awesome shortcuts to see if a number is composite without doing painful long division. They're like secret spy codes! If a number ends in an even digit, you know it's divisible by 2. If its digits add up to a multiple of 3, then 3 is a factor. It’s the quickest way to find a number’s factors and expose it!
Common Questions
What are divisibility tests in math?
Divisibility tests are quick rules that let you determine whether a number can be divided evenly by another number without doing full division. For example, a number is divisible by 2 if its last digit is even.
What are the most common divisibility rules?
A number is divisible by 2 if the last digit is even; by 3 if the sum of digits is divisible by 3; by 5 if the last digit is 0 or 5; by 9 if the sum of digits is divisible by 9; and by 10 if the last digit is 0.
Why are divisibility tests useful in Grade 8?
They speed up simplifying fractions, identifying factors, working with prime factorization, and solving problems involving greatest common factors and least common multiples.
How do you test if a number is divisible by 6?
A number is divisible by 6 if it passes both the divisibility test for 2 (last digit is even) and the test for 3 (sum of digits divisible by 3).
Which textbook covers divisibility tests in Grade 8?
Divisibility tests are taught in Saxon Math Course 3, Chapter 1: Number and Operations and Measurement.