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Multiples of 11: Multiplication with 1-digit number: 11x = 10x + x (Sum of digits=x+x=2x=even) Multiplication with 2-digit number: 11(10x+y) = 110x + 11y = 100x
by ashishb4u 16y ago
Multiples of 11:
Multiplication with 1-digit number:
11x = 10x + x (Sum of digits=x+x=2x=even)
Multiplication with 2-digit number:
11(10x+y) = 110x + 11y = 100x + 10(x+y) + y
If x+y<10, Sum of digits = x+x+y+y=2(x+y)=even
If x+y>=10, 11(10x+y) = 100x + 10(x+y) + y = 100(x+1) + 10 (x+y-10) +y, Sum = x+1+(x+y-10)+y = 2x+2y-9, which is odd.
So, we need to find smallest x+y>=10 where 0<=x,y<10
So, x=1,y=9 and hence the number 11*19=209