# Find the number of divisors of 9600 including 1 and 9600.

$\begin{gathered}

\left( a \right){\text{ 60}} \\

\left( b \right){\text{ 58}} \\

\left( c \right){\text{ 48}} \\

\left( d \right){\text{ 46}} \\

\end{gathered} $

Answer

Verified

385.5k+ views

Hint- Find all the factors of the given number and then try to evaluate the total number of divisors from these factor representations.

First find all the factors of 9600 are

$9600 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5$

We can also write this down as

$9600 = {2^7} \times {3^1} \times {5^2}$……………………………… (1)

Now if a number has factors of the form ${a^p} \times {b^q} \times {c^r}.........{z^m}$then the divisors of that numbers can be written as$\left( {p + 1} \right) \times \left( {q + 1} \right) \times \left( {r + 1} \right)........... \times \left( {m + 1} \right)$.

Using the same concept in equation (1) we get the total number of divisors of 9600 and it includes 1 and the number itself.

$ \Rightarrow \left( {7 + 1} \right) \times (1 \times 1) \times (2 \times 1)$

$ \Rightarrow 8 \times 2 \times 3 = 48$

Hence the correct option is (c).

Note- Whenever we face such a problem statement the key concept involved is simply to find all the factors of the given number now through those factors we can directly find the total number of divisors using the above mentioned concept. The note point here is this number of divisors obtained will always include 1 and the number itself.

First find all the factors of 9600 are

$9600 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5$

We can also write this down as

$9600 = {2^7} \times {3^1} \times {5^2}$……………………………… (1)

Now if a number has factors of the form ${a^p} \times {b^q} \times {c^r}.........{z^m}$then the divisors of that numbers can be written as$\left( {p + 1} \right) \times \left( {q + 1} \right) \times \left( {r + 1} \right)........... \times \left( {m + 1} \right)$.

Using the same concept in equation (1) we get the total number of divisors of 9600 and it includes 1 and the number itself.

$ \Rightarrow \left( {7 + 1} \right) \times (1 \times 1) \times (2 \times 1)$

$ \Rightarrow 8 \times 2 \times 3 = 48$

Hence the correct option is (c).

Note- Whenever we face such a problem statement the key concept involved is simply to find all the factors of the given number now through those factors we can directly find the total number of divisors using the above mentioned concept. The note point here is this number of divisors obtained will always include 1 and the number itself.

Recently Updated Pages

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

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

Which one of the following places is unlikely to be class 8 physics CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

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

Elucidate the structure of fructose class 12 chemistry CBSE

What is pollution? How many types of pollution? Define it