Q27. For any choices of values of X, Y and Z, the 6 digit number of the form XYZXYZ is divisible by:
Detailed Solution
A 6-digit number of the form XYZXYZ can be expressed mathematically as: XYZXYZ = XYZ × 1000 + XYZ = XYZ × (1000 + 1) = XYZ × 1001 Now, we need to find the prime factors of 1001. 1001 can be divided by 7: 1001 ÷ 7 = 143.
143 can be divided by 11: 143 ÷ 11 = 13. 13 is a prime number. So, the prime factorization of 1001 is 7 × 11 × 13. Therefore, any number of the form XYZXYZ is always divisible by 7, 11, and 13.
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