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If a, b, and c are distinct digits, can the three digit numbers a b c and c b a both be divisible by 7? If Yes, what number?

User Luiscubal
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1 Answer

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Given

a, b, and c are distinct digits

Find

numbers abc and cba both be divisible by 7? If yes , then mention the number.

Step-by-step explanation

For divisibility of 7 , the last digit must be from 1 , 3 , 7 and 9

Let the possible number is abc , then cba will also be divisible by 7.

so , we can write it as ,

100a + 10b + c = 7x

100c + 10b + a = 7y

subtract both equations ,

100a+ 10b + c - 100c - 10b - a = 7x - 7y

99a - 99c = 7(x - y)

99(a - c) = 7(x - y)

hence , 99(a - c) must be divisible by 7 .

since 99 is not divisible 7 , (a - c) will be divisible by 7.

hence , only possible values of (a - c) are 0 and 7.

if a - c = 0 then a = c which is not possible as all digits are different.

if a - c = 7

possible values are a = 9 , 8 and c = 2 , 1

hence , multiples of 7 in the form is abc with a = 9 , 8 and c = 2 , 1 are

168 , 259 and their reverse are 861 and 952.

Final Answer

Hence ,

yes , there are numbers abc and cba which can be divisible by 7.

numbers are 168 , 259 and reverse is 861 and 952

User Dissidia
by
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