Evaluate

372567

Factor

3\times 13\times 41\times 233

Copy

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\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\end{array}

First line up the numbers vertically and match the places from the right like this.

\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\phantom{\times99}2097\\\end{array}

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 699 with 3. Write the result 2097 at the end leaving 0 spaces to the right like this.

\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\phantom{\times99}2097\\\phantom{\times9}2097\phantom{9}\\\end{array}

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 699 with 3. Write the result 2097 at the end leaving 1 spaces to the right like this.

\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\phantom{\times99}2097\\\phantom{\times9}2097\phantom{9}\\\underline{\phantom{\times}3495\phantom{99}}\\\end{array}

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 699 with 5. Write the result 3495 at the end leaving 2 spaces to the right like this.

\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\phantom{\times99}2097\\\phantom{\times9}2097\phantom{9}\\\underline{\phantom{\times}3495\phantom{99}}\\\phantom{\times}372567\end{array}

Now add the intermediate results to get final answer.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

Linear equation

y = 3x + 4

Arithmetic

699 * 533

Matrix

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}