The letters a,b and c stand for non-zero digits. The integer abc is a multiple of 3 the integer cbabc is a multiple of 15, and the integer abcba is a multiple of 8. What is the value of the integer cba?


Answer:

576

Step by Step Explanation:
  1. We know that a number is divisible by 8 if it's last 3 digits are divisible by 8.
    Given, abcba is a multiple of 8.
    Therefore cba is a multiple of 8.
  2. Also, abc is given to be a multiple of 3.
    Since the sum of the digits of abc and cba are the same, cba is also a multiple of 3.
    Therefore, cba is a multiple of 24.
  3. We are given that cbabc is a multiple of 15 and c0 (given).
    c=5
    Now, cbabc is a multiple of 15 therefore cbabc is a multiple of 3.
    sum of digits of cbabc is a multiple of 3.
    Also, a+b+c is a multiple of 3, therefore, c+b is a multiple of 3.
  4. The three-digit multiples of 24 starting with 5, which are the possible values of cba are 504,528,552, and 576.
    Out of the above possible values of cba, only 576 has c+b as a multiple of 3.
  5. Hence, the value of the integer cba is 576.

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