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Question
Test the divisibility of the following number by 11:
137269
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Solution
A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
137269 is divisible by 11.
Sum of the digits at odd places = (9 + 2 + 3) = 14
Sum of the digits at even places = (6 + 7 + 1) = 14
Difference of the two sums = (14 − 14) = 0, which is divisible by 11.
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Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no):
|
Number |
Divisible by |
||||||||
|
2 |
3 |
4 |
5 |
6 |
8 |
9 |
10 |
11 |
|
|
128 |
Yes |
No |
Yes |
No |
No |
Yes |
No |
No |
No |
|
990 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
|
1586 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
|
275 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
|
6686 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
|
639210 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
|
429714 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
|
2856 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
|
3060 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
|
406839 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
Why are divisibility tests useful?
