Question 11 of 17intermediate🔍 AnalyzeLong Answer4 marks

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.

Correct Answer

Answer: Dividing abcabc by 7, then by 11, and finally by 13 gives back the original 3-digit number abc.

Why it works: Step 1: abcabc = abc × 1000 + abc = abc × 1001

Step 2: 7×117 \times 11 × 13 = 1001

Step 3: ∴ abcabc = abc × 7×117 \times 11 × 13

Step 4: Dividing by 7, 11, and 13 gives abc

Exercise: Figure it Out (Section 3) | Q: 4 | (Chapter: Page 11)
For More Understanding

Explanation

The chapter provides the hint to multiply 7, 11, and 13. Their product is 1001. A 6-digit number formed by repeating a 3-digit number (abcabc) equals abc × 1000 + abc = abc × 1001. Therefore, dividing by 7, 11, and 13 successively gives back abc.

Solution Steps

  1. Step 1: Express abcabc = abc × 1000 + abc = abc × 1001

  2. Step 2: Calculate 7×117 \times 11 × 13 = 1001

  3. Step 3: Therefore abcabc = abc × 7×117 \times 11 × 13

  4. Step 4: Dividing by 7, 11, and 13 gives abc

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