For any choices of values of X,Y and Z, the 6 digit number of the form XYZXYZ is divisible by :

Question

Accepted Answer

The 6-digit number XYZXYZ can be written as XYZ * 1000 + XYZ.
This simplifies to XYZ * (1000 + 1) = XYZ * 1001.

Now, we need to find the prime factors of 1001.
1001 divided by 7 is 143.
143 divided by 11 is 13.
So, 1001 = 7 * 11 * 13.

Therefore, the number XYZXYZ = XYZ * 7 * 11 * 13.
This shows that the number XYZXYZ is always divisible by 7, 11, and 13, regardless of the values of X, Y, and Z.

Analyzing the options:
A) 7 and 11 only - Incorrect, it is also divisible by 13.
B) 11 and 13 only - Incorrect, it is also divisible by 7.
C) 7 and 13 only - Incorrect, it is also divisible by 11.
D) 7, 11 and 13 - Correct, as the number is a product of XYZ and 7, 11, and 13.

The final answer is D.

Answer

7 and 11 only

Answer

11 and 13 only

Answer

7 and 13 only

Answer

7, 11 and 13

For any choices of values of X,Y and Z, the 6 digit number of the form XYZXYZ is divisible by :

Explanation

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