
Knowing divisibility rules is one element of a Mathnasium mathlete’s number sense, and one of the Pre-Algebra 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
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If
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Example
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2
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The number ends with an even number
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156 because it ends with an even number
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3
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The sum of the digits can be divided by 3
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156 because 1+5+6=12, and 12 can be divided evenly by 3
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4
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The last two digits can be divided by 4
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344 because 44 can be divided evenly by 4
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5
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The number ends with a 0 or 5
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120, 615
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6
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The number can be divided by both 2 and 3
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318 – because it ends with an even number and 3+1+8=12 so it can be divided by 3
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9
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The sum of the digits can be divided by 9
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738 because 7+3+8=18
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10
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The number ends with 0
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730
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12
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The number can be divided by both 3 & 4
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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)
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15
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The number can be divided by both 3 & 5
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20
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The last two digits can be divided by 20
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400 can be divided by 20, 25, and 50 because the last two digits (00) can be divided by 20, 25, and 50
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25
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The last two digits can be divided by 25
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50
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The last two digits can be divided by 50
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11 (test 1)
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The 3-Digit Rule: the sum of the first and last digits equals the middle digit
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792 because 7+2=9
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11 (test 2)
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The General Rule: if the difference of the sum of alternating digits can be divided by 11
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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.
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11 (test 3)
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The Double-Digit 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.
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6,127 because (27) + (61) = 88, which is divisible by 11.
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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 math-only 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 403-872 MATH (6284).
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