Number theoryy

Think of a number, with which if I multiply a three digit number, the product will be the three digit number followed by the three digit number.

If you didn't get that, find x x which satisfies a b c × x = a b c a b c \overline{abc}\times x=\overline{abcabc}


The answer is 1001.

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1 solution

Palash Som
Apr 9, 2015

in the question we need to find x which can satisfy the given situation so let there be a 3 digit number abc such that abc =100a + 10b + c, then abcabc = 100000a + 10000b +1000c +100a + 10b +c we can write it as 100100a + 10010b + 1001c . so we can write the complete statement as 100a+10b+c * x = 1000(100a+10b+c)+(100a+10b+c) . which after solving will become as x = 1000 * 1 +1 = 1001 and 1001 is our answer

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