A six-digit number is formed by repeating a three-digit number. For example 256256, 678678, etc. Any number of this form is divisible by
(a) 7 only
(b) 11 only
(c) 13 only
(d) 1001

Solution:

Let the number be abcabc

On examining the number we can see that difference of the sum of digits in the alternate positions is zero.

abcabc = (a + c + b ) - (b + a + c) = 0

Since the difference is zero the number is divisible by 11.

Such a six digit number is also divisible by 7 and 13.

256256 divided by 7 = 36608

256256 divided by 13 = 19712

Similarly 678678 is divisible by 7 and 13.

11 × 7 × 13 = 1001

Hence such numbers are divisible by 1001

The answer is (d)

✦ Try This: If eight digit number is formed placing a four digit number one after the other but the latter four digits are placed in reversed manner (12344321) then the eight digit number is divisible by. (a) 7 only, (b) 11 only, (c) 13 only, (d) 1001

Let the number be abcd. The eight digit number formed is abcddcba. The difference of the sum of the digits in alternate positions is shown below:

a + c + d + b - (b + d + c + a) = 0

Hence the eight digit number is divisible by 11.

The right answer is (b) 11 only.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16

NCERT Exemplar Class 8 Maths Chapter 13 Problem 10

A six-digit number is formed by repeating a three-digit number. For example 256256, 678678, etc. Any number of this form is divisible by (a) 7 only, (b) 11 only, (c) 13 only, (d) 1001

Summary:

If a six-digit number is formed by repeating a three-digit number it is divisible by 1001. Choice (d).

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