Long Division With Missing Digits

Logic Level 1

Find the sum of all (individual) missing digits that satisfy the long division above.

The answer is 15.

1 solution

Pham Khanh
Sep 5, 2016

Because $23$ is a prime number and the divisor is a 2-digit number so the quotient must be $1$ . $\text{Hence, the divisor = 23 \& dividend = 27}$ . The answer is $2+7+2+3+1=\Large \boxed{\color{#20A900}{15}}$

Moderator note:

Yes, identifying that 23 is prime number shows that the the blue squares (below) must be 23 as well, as $\color{#3D99F6}{\square\square} \; \times \color{grey}{\square } \; = \; \color{#20A900}{\boxed2 \boxed3}$ .

$\LARGE{ \begin{array}{rll} \phantom{0}\ \color{grey}{\boxed{\phantom{0}}} && \\[-2pt] \color{#3D99F6}{ \boxed{{\phantom{0}}} \ \boxed{{\phantom{0}}}}\ \enclose{longdiv}{\color{#D61F06}{\boxed{\phantom{0}} \ \boxed{\phantom{0}}}}\kern-.2ex \\[-2pt] \underline{\color{#20A900}{\boxed{2} \ \boxed{3}}} && \\[-2pt] \boxed{{4}} \end{array} }$

Why is it important for 23 to be prime?

Agnishom Chattopadhyay - 4 years, 9 months ago

Because, the number 23 = divisor $\times$ the only digit, and it's a prime. So, there exists a number, the divisor or the quotient, equals to 1. But, the divisor is a 2-digit number. Hence, the quotient must be equal to 1

Pham Khanh - 4 years, 9 months ago

Long Division With Missing Digits

The answer is 15.

1 solution

Moderator note:

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