Solve 123456789\times987654321 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$123456789 \times 987654321$$

Evaluate

$121932631112635269$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\end{array}$$

Now multiply the first number with the $1^{st}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 1. Write the result 123456789 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\end{array}$$

Now multiply the first number with the $2^{nd}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 2. Write the result 246913578 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\end{array}$$

Now multiply the first number with the $3^{rd}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 3. Write the result 370370367 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\phantom{\times}370370367\phantom{99}\\\end{array}$$

Now multiply the first number with the $4^{th}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 4. Write the result 493827156 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\phantom{\times}370370367\phantom{99}\\\phantom{\times}493827156\phantom{999}\\\end{array}$$

Now multiply the first number with the $5^{th}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 5. Write the result 617283945 at the end leaving 4 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\phantom{\times}370370367\phantom{99}\\\phantom{\times}493827156\phantom{999}\\\phantom{\times}617283945\phantom{9999}\\\end{array}$$

Now multiply the first number with the $6^{th}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 6. Write the result 740740734 at the end leaving 5 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\phantom{\times}370370367\phantom{99}\\\phantom{\times}493827156\phantom{999}\\\phantom{\times}617283945\phantom{9999}\\\phantom{\times}740740734\phantom{99999}\\\end{array}$$

Now multiply the first number with the $7^{th}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 7. Write the result 864197523 at the end leaving 6 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\phantom{\times}370370367\phantom{99}\\\phantom{\times}493827156\phantom{999}\\\phantom{\times}617283945\phantom{9999}\\\phantom{\times}740740734\phantom{99999}\\\phantom{\times}864197523\phantom{999999}\\\end{array}$$

Now multiply the first number with the $8^{th}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 8. Write the result 987654312 at the end leaving 7 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\phantom{\times}370370367\phantom{99}\\\phantom{\times}493827156\phantom{999}\\\phantom{\times}617283945\phantom{9999}\\\phantom{\times}740740734\phantom{99999}\\\phantom{\times}864197523\phantom{999999}\\\phantom{\times}987654312\phantom{9999999}\\\end{array}$$

Now multiply the first number with the $9^{th}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 123456789 with 9. Write the result 1111111101 at the end leaving 8 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\phantom{\times}370370367\phantom{99}\\\phantom{\times}493827156\phantom{999}\\\phantom{\times}617283945\phantom{9999}\\\phantom{\times}740740734\phantom{99999}\\\phantom{\times}864197523\phantom{999999}\\\phantom{\times}987654312\phantom{9999999}\\\underline{\phantom{\times}1111111101\phantom{99999999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times}123456789\\\underline{\times\phantom{}987654321}\\\phantom{\times}123456789\\\phantom{\times}246913578\phantom{9}\\\phantom{\times}370370367\phantom{99}\\\phantom{\times}493827156\phantom{999}\\\phantom{\times}617283945\phantom{9999}\\\phantom{\times}740740734\phantom{99999}\\\phantom{\times}864197523\phantom{999999}\\\phantom{\times}987654312\phantom{9999999}\\\underline{\phantom{\times}1111111101\phantom{99999999}}\\\phantom{\times}-67153019\end{array}$$

Factor

$3^{4}\times 17^{2}\times 3607\times 3803\times 379721$