Playing with Numbers
Category : 8th Class
Playing with Numbers
abc \[=a\times 100+b\times 10+c.\]
Divisibility |
Conditions |
Example |
2. |
The last digit is 0 or an even number |
9340 0 (Last digit 0) 3456 6 (Last digit is an even number) \[\therefore \]9340 & 3456 are divisible by 2.
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3. |
The sum of all the digits of the number is divisible by 3. |
4746 (4+7+4++6)+3 =21+\[\div \]3=7 \[\therefore \]4746 is divisible by 3 |
4. |
The number formed by last two digits of the number is divisible by 4 or are 00.
|
616 16 \[\div \] 4 = 4 8900 00 (Last two digits are 00) \[\therefore \]616 and 8900 are divisible by 4. |
5 |
The last digit of the number is 0 or 5. |
60415 5 (Last digit is 5) 76290 0 (Last digit is 0) \[\therefore \]60415 and 76 290 are divisible by 5.
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6. |
The last digit is 0 or an even number, and the sum of all the digits of the by 6. |
7596 (7+5+9+6)-3 = 27 - 3 = 9 \[\therefore \]7596 is divisible by 6.
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7. |
The difference between the number formed by the digit/digits in front and the doubled value of the last digit is 0 (or) is divisible |
406 406 is divisible by 7 because 40 - (6 x 2) = 28 28 is divisible by 7. \[\therefore \]406 is divisible by 7. 8722 is divisible by 7 because 872 -(2x2)= 868 868 is divisible by 7. \[\therefore \]8722 is divisible by 7. 815 815 is not divisible by 7 because 81 - (5 x 2) = 71 71 is not divisible by 7. \[\therefore \]815 is not divisible by 7.
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8. |
The number formed by the last three digits of the number is divisible by 8. |
3568 568 \[\div \] 8 = 71 \[\therefore \]3568 is divisible by 8. |
9. |
The sum of all the digits of the number is divisible by 9. |
6048 (6+0+4+8)-9= 18-9=2 \[\therefore \]6 048 is divisible by 9. |
10. |
The last digit is 0. |
9310 0 (Last digit is 0) \[\therefore \]9 310 is divisible by 10. |
11. |
The difference of the sum of the digits in even places and the sum of the digits in odd places is 0 or is divisible by 11.
|
1364 ((3 + 4) - (1 + 6)) = 0 3729 ((7 + 9) - (3 + 2)) = 11 \[\therefore \]1364 and 3 729 are divisible by 11. 25176 ((5 + 7) - (2 + 1 + 6)) = 3 \[\therefore \]25176 is not divisible by 11. |
12. |
The number is divisible by both 3 and 4. |
648 (6 + 4 + 8 = 18 and also 48 \[\div \]4=12) \[\therefore \]648 is divisible by 12. 916 (9+1+6= 16 and 16\[\div \]4=4 \[\therefore \]916 is not divisible by 12 as it is not divisible by 3.
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