Question

If a, b, c are three digits of a three-digit number, prove that abc + cab + bca is a multiple of 3.

Answer 1

Answer

Step-by-step explanation:

A number is divisible by 3

Sum of the digits is divisible by 3

a + b + c is a multiple of 3.

Hence b + c + a and c + a + b are multiples of 3. = a + b + c + b + c + a + c + a + b

= 3a + 3b + 3c = 3 (a +b + c) a + b + c is divisible by 3.

Hence it is a multiple of 3.

∴ 3 (a + b + c) is a multiple of 9.

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