Question

# $\text{(abcabc)÷(abc)=____}$ where,$\text{abc}$ represents any $3$ digit number.

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Solution

## Finding $\text{(abcabc)÷(abc)=____}$:We can write $\text{abcabc}$ as $\mathrm{abc}×1000+\mathrm{abc}$.Therefore, $\begin{array}{rcl}\mathrm{abcabc}÷\mathrm{abc}& =& \frac{\mathrm{abcabc}}{\mathrm{abc}}\\ & =& \frac{\mathrm{abc}×1000+\mathrm{abc}}{\mathrm{abc}}\\ & =& \frac{\mathrm{abc}×\left(1000+1\right)}{\mathrm{abc}}\\ & =& 1001\end{array}$Hence, $\text{(abcabc)÷(abc)=1001}$.

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