Question 4 - Figure it out - Page 145-147 - Chapter 6 Class 8 - Algebra Play (Ganita Prakash II)

Transcript

Question 4 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.]First, let’s look at the hint It says to multiply 7, 11 and 13 7 × 11 × 13 = 1001 Now, let the 3-digit number 123 So, our 6 digit number is 123123 We can write it as 123123 = 123000 + 123 = 123 × 1000 + 123 = 123 × (1000 + 1) = 123 × 1001 Thus, algebraically we can write number abcabc as abcabc = abc × 1001 = abc × 7 × 11 × 13 Since 7, 11 and 13 are multiplied by some multiple We can write that abcabc is completelty divisible by 7, 11 and 13, leaving remainder 0