Rules of Division | 2-12 |

I will be teaching you how to know if any number is divisible by 2-12, evenly.

Let's start:

2: If the last digit is even, the number is divisible by 2.
Eg. 208 is Divisible by 2, but 209 isn't.

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3: If the sum of the digits is divisible by 3, the number is also.
Eg. Number is 222. 2+2+2=6. 6 is divisible by 3.

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4: If the last two digits form a number divisible by 4, the number is also.
Eg. Number is 1,987,416. 1,987,416. 16 is divisible by 4.

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5: If the last digit is a 5 or a 0, the number is divisible by 5.
Eg. Number is 20,987,985. 20,987,985. This is divisible by 5.

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6: If the number is divisible by both 3 and 2, it is also divisible by 6.
Eg. Number is 2196. 2+1+9+6=18. 18 is divisible by 3.
2196. The number is divisible by 2. Therefore, 2196 is divisible by 6.

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7: Take the last digit, double it, and subtract it from the rest of the number;
If the answer is divisible by 7 (including 0), then the number is also.
Eg: Number is 84. 4+4= 8. 84-8=76. 76 is not divisible by 7, so 84 isn't, either.

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8: If the last three digits form a number divisible by 8, then so is the whole number.
Eg. Number is 1,964,152. 1,964,152. 152 is divisible by 8, therefore 1,964,152 is, also.

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9: If the sum of the digits is divisible by 9, the number is also.
Eg. The same as No. 3, but instead of it being divisible by 3, it has to be divisible by 9.

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10: If the number ends in 0, it is divisible by 10.
Eg. Number is 1,768,420. 1,768,420. 420 ends in a 0, which means it is divisible by 10.

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11: Alternately add and subtract the numbers from left to right. (You can think of the first digit as being 'added' to zero.)
If the result (including 0) is divisible by 11, the number is also.
Eg: To see whether 498,291,398 is divisible by 11, do this:
[0+]4-9+8-2+9-1+3-9+8 = 11; therefore 498,291,398 is divisible by 11.

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12: If the number is divisible by both 3 and 4, it is also divisible by 12.
Eg. Number is 180. 180 is divisible by 3 and 4, therefore it is divisible by 12.

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Good guide. Can't really expand on the topic so you did good.

 

Thanks.