What's the number?

Number Theory Level 2

What least number should be replaced instead of the x x such that it is divisible by the number eleven, 14578456 x 34 ‾ \overline{14578456x34} .


The answer is 1.

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Bhargav Y by Bhargav Y , 18, India

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2 solutions

Mahdi Raza
May 13, 2020

1 4 5 7 8 4 5 6 x 3 4 {\color{#3D99F6}{1}}{\color{#D61F06}{4}}{\color{#3D99F6}{5}}{\color{#D61F06}{7}}{\color{#3D99F6}{8}}{\color{#D61F06}{4}}{\color{#3D99F6}{5}}{\color{#D61F06}{6}}{\color{#3D99F6}{x}}{\color{#D61F06}{3}}{\color{#3D99F6}{4}}

11 ∣ ( 1 + 5 + 8 + 6 + x + 4 ) − ( 4 + 7 + 4 + 6 + 3 ) 11 | {\color{#3D99F6}{\bigg(1 + 5 + 8 + 6 + x + 4\bigg)}} - {\color{#D61F06}{\bigg(4 + 7 + 4 + 6 + 3\bigg)}}

11 ∣ x − 1 x ∈ { 0 , 1 , 2 , … 9 } 11 | x - 1 \quad x \in \{0, 1, 2, \ldots 9\}

x = 1 \boxed{x = 1}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Natanael Flores
Feb 20, 2016

(3+6+4+7+4)-(1+5+8+5+4+x)

If we make x=1

24-24=0

So x=1 is the searched value

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I was a bit confused by the wording. Maybe it could say something like:

What is the smallest value of x x which would make 14578456 x 34 ‾ \overline{14578456x34} divisible by 11 11 ?

Marta Reece - 3 years, 5 months ago

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