Show that pos int divisible by 3 iff sum of digits divisible by 3

Show that a positive integer is divisible by 3 iff the sum of its digits is divisible by 3.

This is from Rosen but I can't follow the proof in the solutions manual (again). Section 3.6 problem 29.

Please explain the detail so I'll understand the whole process.

Re: Show that pos int divisible by 3 iff sum of digits divisible by 3

Let a number be abc

= 100a + 10b + c

= 99a + 9b + a + b + c

99a and 9 b are divisible by 3

so (a + b + c) must be divisible by 3.

so (a + b + c) is sum of digits must be divisible by 3.

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