Consider any 3-digit number, say abc. Make it a 6-digit number by repeating the digits, that is abcabc. Class 8

Consider any 3-digit number, say abc. Make it a 6-digit number by repeating the digits, that is abcabc. Class 8

Question 1.

Consider any 3-digit number, say abc. Make it a 6-digit number by repeating the digits, that is abcabc. Divide this number by 7, then by 11, and finally by 13. What do you get? Try this with other numbers. Figure out why it works. [Hint: Multiply 7, 11 and 13.] Class 8

Solution:

Le the number be abcabc.

= 100000a + 10000b + 1000c + 100a + 10b + c

= 100100a + 10010b + 1001c

= 1001 (100a + 10b + c)

= 7 × 11 × 13 (100a + 10b + c)

So, the number is divisible by 7, 11 and 13.