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Question
Which of the following numbers is divisible by 6?
(a) 8790432
(b) 98671402
(c) 85492014
(d) none of these
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Solution
(a) 8790432 and (c) 85492014
A number is divisible by 6 if it is divisible by both 2 and 3.
(a) 8790432
Consider number 8790432.
The number in the ones digit is 2.
Therefore, 8790432 is divisible by 2.
Now, the sum of its digits (8+7+9+0+2+3+2) is 33. Since 33 is divisible by 3, we can say that 8790432 is also divisible by 3.
Since 8790432 is divisible by both 2 and 3, it is also divisible by 6.
(b) 98671402
Consider the number 98671402.
The number in the ones digit is 2.
Therefore, 98671402 is divisible by 2.
Now, the sum of its digits (9+8+6+7+1+4+0+2) is 37. Since 37 is not divisible by 3, we can say that 98671402 is also not divisible by 3.
Since 98671402 is not divisible by both 2 and 3, it is not divisible by 6.
(c) 85492014
Consider the number 85492014.
The number in the ones digit is 4.
Therefore, 85492014 is divisible by 2.
Now, the sum of its digits (8+5+4+9+2+0+1+4) is 33. Since 33 is divisible by 3, we can say that 85492014 is also divisible by 3.
Since 85492014 is divisible by both 2 and 3, it is also divisible by 6.
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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 |
______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ | ______ |
