Question
In the following numbers. replace * by the smallest number to make it divisible by 11:
9 × 8071
9 × 8071
✓
Answer
Rule: A number is divisible by 11 if the difference of the sums of the alternate digits is either 0 or a multiple of 11.
9 × 8071
Sum of the digits at the odd places = 9 + 8 + 7 = 24
Sum of the digits at the even places = missing number + 0 + 1 = missing number + 1
Difference = 24 - [missing number + 1] = 23 - missing number
According to rule, 23 - missing number = 22 [Because 22 is a multiple of 11 and the missing number is a single digit]
Thus, missing number = 1
Hence, the smallest required number is 1.
9 × 8071
Sum of the digits at the odd places = 9 + 8 + 7 = 24
Sum of the digits at the even places = missing number + 0 + 1 = missing number + 1
Difference = 24 - [missing number + 1] = 23 - missing number
According to rule, 23 - missing number = 22 [Because 22 is a multiple of 11 and the missing number is a single digit]
Thus, missing number = 1
Hence, the smallest required number is 1.
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