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Let us say the 3 digit natural number is A B C (like 674). A,B,C are digits and A is not 0.

Then Value of ABC = 12 * (A+B+C)

100 * A + 10 * B + C = 12 * (A+B+C) = 12 A + 12 B + 12 C

That means C is even as 8A is even.

A >= 1 That means 88A >= 88. But 2B <=18. That means 11C > 70.

88A = 2 B + 88 44A = B + 44 B = 44(A-1)

This is possible only if A = 1 and B=0. For A>1, B is > 9 which is not possible.

Then Value of ABC = 12 * (A+B+C)

100 * A + 10 * B + C = 12 * (A+B+C) = 12 A + 12 B + 12 C

__So__**88 A = 2 B + 11 C****Means 8A - C is even.***2 B = 11 (8A - C)*That means C is even as 8A is even.

*Choose numbers with C as even: 0,2,4,6,8*A >= 1 That means 88A >= 88. But 2B <=18. That means 11C > 70.

****That means C >= 7. So C = 8 only.**

88A = 2 B + 88 44A = B + 44 B = 44(A-1)

This is possible only if A = 1 and B=0. For A>1, B is > 9 which is not possible.

**ONLY ONE SOLUTION 108**