Consider a 3 digit integer x with distinct digits

Asked by admin @ in Math viewed by 4799 People

Consider a 3-digit integer x with distinct digits. Let y be the integer formed by swapping

x's units and hundreds digits. What is the greatest prime number less than 30 thatperfectly divides the absolute difference between x and y?​

Answered by admin @


Given :  3-digit integer x with distinct digits.

y be the integer formed by swapping x's units and hundreds digits.

To Find : the greatest prime number less than 30 that perfectly divides the absolute difference between x and y

Solution:

3-digit integer x with distinct digits.   =  abc

100a + 10b + c

y be the integer formed by swapping x's units and hundreds digits.

=> cba

100c + 10b + a

Difference  =  100a + 10b + c - (100c + 10b + a)

= 99a  - 99c

= 99(a - c)

= 3 * 3 *11 (a - c)

11  is the greatest prime number that perfectly divides the absolute difference between x and y

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