Knowing divisibility rules is one element of a Mathnasium mathlete’s number sense, and one of the PreAlgebra Checklist. Before learning about divisibility rules, a child should know multiplication facts first. How to learn multiplication? We don’t suggest memorizing times tables but using strategies like we explained in our blog: Tips for Parents: How to teach Multiplication Facts.
Knowing divisibility rules will help students to find whether a given number is divisible by a fixed number with greater ease, and help them to build their understanding of numbers.
Test for Divisibility
A number is divisible by

If

Example

2

The number ends with an even number

156 because it ends with an even number

3

The sum of the digits can be divided by 3

156 because 1+5+6=12, and 12 can be divided evenly by 3

4

The last two digits can be divided by 4

344 because 44 can be divided evenly by 4

5

The number ends with a 0 or 5

120, 615

6

The number can be divided by both 2 and 3

318 – because it ends with an even number and 3+1+8=12 so it can be divided by 3

9

The sum of the digits can be divided by 9

738 because 7+3+8=18

10

The number ends with 0

730

12

The number can be divided by both 3 & 4

180 can be divided by 12 & 15 because it can be divided by 3 (see the sum of the digits), by 4 (the last 2 digits, 80, is divisible by 4), and by 5 (it ends with a 0)

15

The number can be divided by both 3 & 5

20

The last two digits can be divided by 20

400 can be divided by 20, 25, and 50 because the last two digits (00) can be divided by 20, 25, and 50

25

The last two digits can be divided by 25

50

The last two digits can be divided by 50

11 (test 1)

The 3Digit Rule: the sum of the first and last digits equals the middle digit

792 because 7+2=9

11 (test 2)

The General Rule: if the difference of the sum of alternating digits can be divided by 11

9,361 can be divided by 11 because: (9+6) – (3+1) = 11, which is divisible by 11.
Note: 0 is a multiple of 11.

11 (test 3)

The DoubleDigit Rule: starting at the decimal point, group the digits of the number in pairs, add the pairs together. If the sum is divisible by 11, the number is divisible by 11.

6,127 because (27) + (61) = 88, which is divisible by 11.

Divisibility rules are also useful in finding whether a number is a multiple of another number or a prime number. This is very helpful when trying to reduce a fraction, factoring, or solving other problems with large numbers, thus minimizing too much trial and error.
For videos on Divisibility:
Does your child need extra support in math? Mathnasium of Red Deer is your neighbourhood’s mathonly learning centre, and we are here to unlock your child’s potential and set them on a path to lifetime success. Our centre director, Riwan, and the whole team, would be happy to meet you! We are conveniently located in the shopping destination area in Red Deer: 5250 22nd St, Unit 30 B – at the Gaetz Avenue Crossing shopping centre, in the same area as Chapters Indigo/Starbucks, Michael Arts, Petland and Ashley, and the phone number is 403872 MATH (6284).
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