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Divisibility RulesIf you know these rules you will look like a math- a-magician

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Dividing by 2’s

• You can divide by 2 if the last digit is even

• 0,2,4,6,8 are even numbers• Example: 128 is ________ by ___• Non Example 129 is ____ ______ by ___

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Divisible by 3.

• You can divide a number by three if the sum of its digits is divisible by 3

• Example: 123, 1 + 2 + 3 =____ and ___ is _______ by ____

• Non Example 125: 1+ 2+5=____, ___ is ____ _______by ____

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Divisible by 4

• A number is divisible by 4 if the last two digits are divisible by 4

• Example 1,312. ____ is ______ by ____, so 1,312 is ______ by ___

• Non Example 2,423. ____ is _____ ______ by ___ so 2,423 is _____ ______ by ___

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• If a number is divisible by 5, then the last digit is either 0 or 5.

• Example: 1,230. ____ is the last digit so 1,230 is divisible by 5.

• Non Example: 1,346. ____ is the last digit and ___ is not ______ or ____ so 1,346 is _____ ______ by _____

Divisible by 5.

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• A number is divisible by 6 if the sum of the digits is divisible by both 2 and 3

• Example: 114 (it is ____ so divisible by ____, and 1+1+4=____and 6÷3 = ___) so it is _____________ by ____.

• Non Example: 308 (it is _____ so it is __________ by ___, but 3+0+8=____ and 11÷3 = ____) so 308 is ____ _______ by _____

Divisible by 6.

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• A number is divisible by 7 if you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7 (Note: you can apply this rule to that answer again if you want)

• Example: 672 (Double ____ is ___, 67-____=___, and ___÷___=___) So 672 is _________ by 7

• Non Example : 905 (Double ____ is ____, ___-___=___, and ____÷7=___) So 905 is ____ _________ by _____

Divisible by 7

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• A number is divisible by 8 if the last three digits are divisible by 8

• Example:109,816 (_____÷____=____ ) so 109,816 is _______ by _______

• Non Example: 216,302 (_____÷____=_____) So 216,302 is _____ _________ by _____

• An alternate way is to apply the rule for “4”. If your result is even,

• your number is divible by 8.

Divisible by 8.

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• A number is divisible by 9 if the sum of the digits is divisible by 9

• Example: 1629 (1+6+2+9=______, and again, _____=____) So ____ is _________ by ______

• Non Example: 2013 (2+0+1+3=___) and _____ is ____ ________ BY _____

Divisible by 9.

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• A number is divisible by 10 if the last digit is zero.

• Example 14,360. The last digit is ____, so 14,360 is _______ by____

• Non Example 15,609. The last digit is ________, so 15, 609 is ____ ________ by _____

Divisible by 10

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• A number is divisible by 11 if you sum every second digit and subtract the rest and the result is zero of divisible by 11

• Example: 1364: 3+4 –(1+6) =___ so 1364 is ______ by ____

• Non Example 1365: 3 + 5 –(1+6) = ____ so 1365 is ___ ______ by _____

Divisible by 11 or 12

• A number is divisible by 12 if the number is divisible by both 3 and 4.

• Example: 1524: 24 is divisiby by 4. 1+5+2+4 = ____. So 1524 is ________ by ____

Non Example 1113: 1+1+1+3= ____, divisible by 3, but 13 is ___ ______ by ___.