Question
Download Solution PDFAny six-digit number that is formed by repeating a three-digit number, is always divisible by:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Let the three digits be P, Q, and R.
Then, the number = PQRPQR
According to the concept,
P × 100000 + Q × 10000 + R × 1000 + P × 100 + Q × 10 + R × 1 = PQRPQR
⇒ 100100P + 10010Q + 1001R = PQRPQR
⇒ 1001(100P + 10Q + R) = PQRPQR
⇒ PQRPQR = 1001 × k (letting (100P + 10Q + R) = k)
Hence, the number is divisible by 1001.
∴ Any six-digit number that is formed by repeating a three-digit number, is always divisible by 1001.
Last updated on Jul 16, 2025
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