Question
Which of the following numbers is divisible by 7 ?
The correct answer is
875
Explanation :-
Applying the Divisibility Rule for 7 :-
The rule states: For a number N, let the last digit be d and the remaining part be R. Calculate R - 2d. If R - 2d is divisible by 7, then N is divisible by 7.
Let's apply this rule to each option:
| Number | Calculation (R - 2d) | Result | Divisible by 7? |
|---|---|---|---|
| 894 | 89 - (2 * 4) = 89 - 8 = 81 | 81 | No (81 / 7 = 11 remainder 4) |
| 87 | 8 - (2 * 7) = 8 - 14 = -6 | -6 | No (-6 / 7 = -1 remainder 1, or simply not a multiple of 7) |
| 875 | 87 - (2 *5) = 87 - 10 = 77 | 77 | Yes (77 / 7 = 11) |
| 687 | 68 - (2 *7) = 68 - 14 = 54 | 54 | No (54 / 7 = 7 remainder 5) |
Conclusion :-
Based on the divisibility rule application:
- 894 is not divisible by 7.
- 87 is not divisible by 7.
- 875 is divisible by 7 because the result (77) is divisible by 7. We can verify this with division: 875 / 7 = 125.
- 687 is not divisible by 7.
Therefore, the number 875 is the one divisible by 7 among the given options.
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Important Questions from Divisibility Rules
Find the least value of x for which 57x716 is divisible by 9.
Which of the following numbers is NOT divisible by 11?
If 321y72 is a multiple of 6, where y is a digit, what is the least value of y?
From the given numbers A, B, C and D, which number is NOT divisible by 11?
A = 712712
B = 177210
C = 64614
D = 756148
- Which of the following numbers is divisible by 71?
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