Divisibility
Divisibility is the ability of one whole number to be divided by another with no remainder. For example, 24 is divisible by 6 because 24 ÷ 6 = 4 with no remainder. Knowing divisibility rules helps you quickly determine factors without long division — for example, a number is divisible by 3 if its digits sum to a multiple of 3. These shortcuts are essential in 7th grade math for simplifying fractions, finding factors, and working with prime numbers. This concept is covered in Saxon Math, Course 2.
Key Concepts
Property The capability of a whole number to be divided by another whole number with no remainder is called divisibility .
Examples Is 3,150 divisible by 6? Yes, because its last digit (0) is even and the sum of its digits ($3+1+5+0=9$) is divisible by 3. Is 724 divisible by 4? Yes, because its last two digits (24) can be divided by 4. Is 724 divisible by 9? No, because the sum of its digits ($7+2+4=13$) is not divisible by 9.
Explanation Divisibility is a math superpower that lets you see if numbers divide evenly without doing the long work! Instead of dividing, you use clever tricks, like checking a number's last digit or the sum of its digits. It’s the ultimate shortcut for spotting factors in big, scary looking numbers and simplifying them quickly.
Common Questions
What is divisibility in math?
Divisibility means one number can be divided by another with no remainder. For example, 18 is divisible by 6 because 18 ÷ 6 = 3 exactly.
What are the divisibility rules?
Key divisibility rules: divisible by 2 if even; by 3 if digits sum to a multiple of 3; by 5 if last digit is 0 or 5; by 10 if last digit is 0; by 6 if divisible by both 2 and 3.
How is divisibility different from division?
Division is the actual calculation of splitting a number into parts. Divisibility is a property — it tells you whether division will result in a whole number with no remainder, without needing to perform the full division.
How does divisibility help with fractions?
Divisibility tests let you quickly find common factors for simplifying fractions. If you can see that both numerator and denominator are divisible by 3, you can simplify without doing full division.
Is 81 divisible by 9?
Yes. Add the digits: 8 + 1 = 9, which is divisible by 9. So 81 is divisible by 9 (81 ÷ 9 = 9).
When do students learn about divisibility?
Divisibility is introduced in 4th–5th grade and extended in 7th grade math, where it connects to prime factorization, GCF, and simplifying fractions.
Which textbook covers divisibility?
Saxon Math, Course 2 covers divisibility rules and their applications.