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Prove if the sum of the digits of a 3 digit number n is divisible by 9, then n is divisible by 9.

Prove if the sum of the digits of a 3 digit number n is divisible by 9, then n is divisible by 9.
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Prove if the sum of the digits of a 3 digit number n is divisible by 9, then n is divisible by 9.

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User HotFrost
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n=100x+10y+z\\x+y+z=9k,k\in\mathbb{Z}\\\\n=99x+9y+x+y+z\\n=99x+9y+9k\\n=9(11x+y+k)

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User MaxYarmolinsky
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