Using the Rules of Divisibility Effectively

These rules will help students look at numbers with greater ease and build their understanding of numbers.
By Jennifer Hogan
May 13, 2014

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8-13

May 13, 2014

There are many "tricks" in math that can help kids solve problems faster and improve overall math skills.  However, as a math teacher, I'm hesitant to show kids these tricks until they fully understand how and why they are using them.  I believe they need to really master a concept before they can use a "trick" effectively.   There are certain stages that I will introduce certain tricks depending on each student and their understanding.  There is however the Rules of Divisibility that I believe all students should understand and be exposed to as early as possible (about 4th grade).  These rules help students to not be afraid of large numbers and can help build number sense.  We want students to feel comfortable with numbers and be flexible working with them.  The rules of divisibility do exactly that!  But I'm amazed when I walk into middle school classrooms and the students have no idea what I'm talking about when I ask them to tell me if a number is divisible by 3 without actually using division.  Many textbooks don't have lessons on the rules of divisibility and many teachers don't teach them, which I think can hurt students.  There is no reason for a student to use a calculator or long division to find if 345 is divisible by 5, but most do!   If your children have not been exposed to the rules of divisibility, I highly suggest you show them these rules.  Have them write each rule on an index card and keep it for homework help each night.

3rd grade is when the concept of multiplication and division is taught, and 4th grade is when students learn about factors/multiples and prime/composite numbers.  They will use this language through high school, so it's important they feel comfortable with them.  These rules will help students look at numbers with greater ease and build their understanding of numbers.

Rules of Divisibility
2:  A number is divisible by 2 if it is even: has a 0, 2, 4, 6, 8 in the ones' place
Ex:    578  is divisible by 2 because an 8 is in the one's place

3: A number is divisible by 3 if: the sum of its digits is divisible by 3
Ex:    384 is divisible by 3 because 3 + 8 + 4 = 15 and 15 is a multiple of 3

4: A number is divisibly by 4 if: the number formed by the last two digits is divisible by 4
Ex:    1,784 is divisible by 4 because 84 is divisible by 4

5: A number is divisible by 5 if: it has a 0 or 5 in the one's place
Ex:    965 is divisible by 5 because there is a 5 in the one's place

6: A number is divisible by 6 if: it is divisible by 2 and 3
Ex:    732 is divisible by 6 because it's even (divisible by 2) and
7 + 3 + 2 = 12 which is divisible by 3

9: A number is divisible by 9 if: the sum of its digits is divisible by 9
Ex:    783 is divisible by 9 because 7 + 8 + 3 = 18 and 18 is divisible by 9

10: A number is divisible by 10 if: it has a 0 in the one's place
Ex:    670 is divisible by 10 because there is a 0 in the one's place

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