A six-digit number is formed by repeating a three-digit number.

Question:

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:

The correct answer is optionĀ 

(d) 1001

Explanation:

From the given question, the number should be of the form abcabc

So the general form of abcabc is 1000000a+100000b+1000c+100a+10b+c

Now, abcabc = is 1000000a+100000b+1000c+100a+10b+c

By simplifying the above expression, we will get

abcabc = 1001(100a+10b+c)

Hence, the six digit number should be divisible by 1001.

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now