How to solve 17432006/5040

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 17432006/5040 | Equatix

Question

$$17432006\div5040$$

Evaluate

$\frac{8716003}{2520}\approx 3458.731349206$

Steps For Long Division Method

Use the $1^{st}$ digit $1$ from dividend $17432006$

$$\begin{array}{l}\phantom{5040)}\phantom{1}\\5040\overline{)17432006}\\\end{array}$$

Since $1$ is less than $5040$, use the next digit $7$ from dividend $17432006$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{5040)}0\phantom{2}\\5040\overline{)17432006}\\\end{array}$$

Use the $2^{nd}$ digit $7$ from dividend $17432006$

$$\begin{array}{l}\phantom{5040)}0\phantom{3}\\5040\overline{)17432006}\\\end{array}$$

Since $17$ is less than $5040$, use the next digit $4$ from dividend $17432006$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{5040)}00\phantom{4}\\5040\overline{)17432006}\\\end{array}$$

Use the $3^{rd}$ digit $4$ from dividend $17432006$

$$\begin{array}{l}\phantom{5040)}00\phantom{5}\\5040\overline{)17432006}\\\end{array}$$

Since $174$ is less than $5040$, use the next digit $3$ from dividend $17432006$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{5040)}000\phantom{6}\\5040\overline{)17432006}\\\end{array}$$

Use the $4^{th}$ digit $3$ from dividend $17432006$

$$\begin{array}{l}\phantom{5040)}000\phantom{7}\\5040\overline{)17432006}\\\end{array}$$

Since $1743$ is less than $5040$, use the next digit $2$ from dividend $17432006$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{5040)}0000\phantom{8}\\5040\overline{)17432006}\\\end{array}$$

Use the $5^{th}$ digit $2$ from dividend $17432006$

$$\begin{array}{l}\phantom{5040)}0000\phantom{9}\\5040\overline{)17432006}\\\end{array}$$

Find closest multiple of $5040$ to $17432$. We see that $3 \times 5040 = 15120$ is the nearest. Now subtract $15120$ from $17432$ to get reminder $2312$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{5040)}00003\phantom{10}\\5040\overline{)17432006}\\\phantom{5040)}\underline{\phantom{}15120\phantom{999}}\\\phantom{5040)9}2312\\\end{array}$$

Use the $6^{th}$ digit $0$ from dividend $17432006$

$$\begin{array}{l}\phantom{5040)}00003\phantom{11}\\5040\overline{)17432006}\\\phantom{5040)}\underline{\phantom{}15120\phantom{999}}\\\phantom{5040)9}23120\\\end{array}$$

Find closest multiple of $5040$ to $23120$. We see that $4 \times 5040 = 20160$ is the nearest. Now subtract $20160$ from $23120$ to get reminder $2960$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{5040)}000034\phantom{12}\\5040\overline{)17432006}\\\phantom{5040)}\underline{\phantom{}15120\phantom{999}}\\\phantom{5040)9}23120\\\phantom{5040)}\underline{\phantom{9}20160\phantom{99}}\\\phantom{5040)99}2960\\\end{array}$$

Use the $7^{th}$ digit $0$ from dividend $17432006$

$$\begin{array}{l}\phantom{5040)}000034\phantom{13}\\5040\overline{)17432006}\\\phantom{5040)}\underline{\phantom{}15120\phantom{999}}\\\phantom{5040)9}23120\\\phantom{5040)}\underline{\phantom{9}20160\phantom{99}}\\\phantom{5040)99}29600\\\end{array}$$

Find closest multiple of $5040$ to $29600$. We see that $5 \times 5040 = 25200$ is the nearest. Now subtract $25200$ from $29600$ to get reminder $4400$. Add $5$ to quotient.

$$\begin{array}{l}\phantom{5040)}0000345\phantom{14}\\5040\overline{)17432006}\\\phantom{5040)}\underline{\phantom{}15120\phantom{999}}\\\phantom{5040)9}23120\\\phantom{5040)}\underline{\phantom{9}20160\phantom{99}}\\\phantom{5040)99}29600\\\phantom{5040)}\underline{\phantom{99}25200\phantom{9}}\\\phantom{5040)999}4400\\\end{array}$$

Use the $8^{th}$ digit $6$ from dividend $17432006$

$$\begin{array}{l}\phantom{5040)}0000345\phantom{15}\\5040\overline{)17432006}\\\phantom{5040)}\underline{\phantom{}15120\phantom{999}}\\\phantom{5040)9}23120\\\phantom{5040)}\underline{\phantom{9}20160\phantom{99}}\\\phantom{5040)99}29600\\\phantom{5040)}\underline{\phantom{99}25200\phantom{9}}\\\phantom{5040)999}44006\\\end{array}$$

Find closest multiple of $5040$ to $44006$. We see that $8 \times 5040 = 40320$ is the nearest. Now subtract $40320$ from $44006$ to get reminder $3686$. Add $8$ to quotient.

$$\begin{array}{l}\phantom{5040)}00003458\phantom{16}\\5040\overline{)17432006}\\\phantom{5040)}\underline{\phantom{}15120\phantom{999}}\\\phantom{5040)9}23120\\\phantom{5040)}\underline{\phantom{9}20160\phantom{99}}\\\phantom{5040)99}29600\\\phantom{5040)}\underline{\phantom{99}25200\phantom{9}}\\\phantom{5040)999}44006\\\phantom{5040)}\underline{\phantom{999}40320\phantom{}}\\\phantom{5040)9999}3686\\\end{array}$$

Since $3686$ is less than $5040$, stop the division. The reminder is $3686$. The topmost line $00003458$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $3458$.

$$\text{Quotient: }3458$$ $$\text{Reminder: }3686$$

Show Solution

Factor

$\frac{19 \cdot 631 \cdot 727}{2 ^ {3} \cdot 3 ^ {2} \cdot 5 \cdot 7} = 3458\frac{1843}{2520} = 3458.731349206349$

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Steps For Long Division Method

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