Answer

Verified

345.6k+ views

**Hint:**To find the prime factors, we will use the ladder method. In this method, we will write the number horizontally on the right within an L-shaped structure. On the left, we will write its prime factors that completely divide the number (starting from the lowest prime number). We will write the quotient below. Then, we will write the prime factors of this quotient on the left of it and the resultant quotient will be written below. We will do this procedure till the quotient becomes 1.

**Complete step by step solution:**

We have to write the prime factors of each of the given numbers. For this, we will be using the ladder method. In this method, we will write the number horizontally on the right and on the left, we will write its prime factors that completely divide the number (starting from the lowest prime number). We will write the quotient below. Then, we will write the prime factors of the quotient on the left of it and the corresponding quotient will be written below. We will do this procedure till the quotient becomes 1.

Now, let us find the prime factors of each of the given numbers.

(i) To find the prime factors of 754, we will use the ladder method described above.

$\begin{align}

& 2\left| \!{\underline {\,

784 \,}} \right. \\

& 2\left| \!{\underline {\,

392 \,}} \right. \\

& 2\left| \!{\underline {\,

196 \,}} \right. \\

& 2\left| \!{\underline {\,

98 \,}} \right. \\

& 7\left| \!{\underline {\,

49 \,}} \right. \\

& 7\left| \!{\underline {\,

7 \,}} \right. \\

& \text{ }\text{ }\text{ }1 \\

\end{align}$

The structure of the ladder method is shown above. We can see that 784 is completely divisible by 2 and the quotient is 392 which is written below 784. Then, we have divided 3942 by 2 (completely divisible) and the quotient is written below, which is 196. We have done this procedure till we obtained 1 at the end.

Therefore, we can write $784=2\times 2\times 2\times 2\times 7\times 7$ .

Hence, the prime factors of 784 are 2 and 7.

(ii) Let us find the prime factors of 12544.

\[\begin{align}

& 2\left| \!{\underline {\,

12544 \,}} \right. \\

& 2\left| \!{\underline {\,

6272 \,}} \right. \\

& 2\left| \!{\underline {\,

3136 \,}} \right. \\

& 2\left| \!{\underline {\,

1568 \,}} \right. \\

& 2\left| \!{\underline {\,

784 \,}} \right. \\

& 2\left| \!{\underline {\,

392 \,}} \right. \\

& 2\left| \!{\underline {\,

196 \,}} \right. \\

& 2\left| \!{\underline {\,

98 \,}} \right. \\

& 7\left| \!{\underline {\,

49 \,}} \right. \\

& 7\left| \!{\underline {\,

7 \,}} \right. \\

& \text{ }\text{ }\text{ }1 \\

\end{align}\]

Therefore, we can write $12544=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 7\times 7$ .

Hence, the prime factors of 12544 are 2 and 7.

**Note:**Students must divide the number and write its factors carefully. They must only use prime numbers in the ladder method. Prime numbers are numbers that have only 2 factors: 1 and themselves. We can also use the factor tree method. In this method, we will write the number at the top and draw two branches. Below one branch will be its prime factor that completely divides the number and below the other branch, we will write its quotient. Now, we will draw two branches for this quotient and repeat the steps until we get two prime numbers in the two last branches.

We can write 784 as

\[\begin{align}

& \begin{matrix}

{} & {} & 784 & {} \\

\end{matrix} \\

& \begin{matrix}

{} & {} & \swarrow \searrow & {} \\

\end{matrix} \\

& \begin{matrix}

{} & \text{ }2 & {} & 394 \\

\end{matrix} \\

& \begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

\text{ }\swarrow \searrow & {} \\

\end{matrix} \\

& \begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

2 & \text{ }196 \\

\end{matrix} \\

& \begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

{} & \text{ }\swarrow \searrow \\

\end{matrix} \\

& \begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

{} & 2 & {} & 98 \\

\end{matrix} \\

& \begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

{} & {} & {} & \swarrow \searrow \\

\end{matrix} \\

& \begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

{} & {} & \text{ }2 & \text{ }\text{ }\text{ }49 \\

\end{matrix} \\

& \begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

{} & {} & \text{ } & \text{ }\swarrow \searrow \\

\end{matrix} \\

& \begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

{} & {} & {} & {} \\

\end{matrix}\begin{matrix}

\text{ }7 & {} & 7 \\

\end{matrix} \\

\end{align}\]

Similarly, we can do 12544.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

How many crores make 10 million class 7 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE