Tag: real numbers on number line

Questions Related to real numbers on number line


$20$ is written as the product of primes as :

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. ${2\times 5 }$

  2. ${2\times 2\times 3\times 5}$

  3. ${2\times 2\times 5}$

  4. ${2\times 2\times 3}$

Show answer
Correct Option: C
Explanation:

To write a number as product of its primes, we divide it by various prime numbers $ 2, 3, 5, 7 $ etc one by one and check by which prime numbers it is divisible with and how many times.

Hence, $ 20 = 2 \times 10 = 2 \times 2 \times 5 $          

In a division sum the divisor is $12$  times the quotient and  $5$  times the remainder. If the remainder is  $48$  then what is the dividend?

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. $2404$

  2. $4808$

  3. $3648$

  4. $4848$

Show answer
Correct Option: D
Explanation:

Divisor $= 5$  $\displaystyle \times $ Remainder = 5 $\displaystyle \times $ $48 = 240$
$\displaystyle \therefore $ Quotient = $\displaystyle \frac{1}{12}\times 240=20$
$\displaystyle \Rightarrow $ Dividend = Divisor $\displaystyle \times $Quotient + Remainder
$= 240 $ $\displaystyle \times $  $ 20 + 48 = 4800 + 48$
$=4848 $

A number $x$ when divided by $7$  leaves a remainder $1$ and another number $y$ when divided by $7$  leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: C
Explanation:
Given numbers $x,y$ 

Let us assume $a$ is the quotient when $x$ is divided by $7$ and $b$ is the quotient when $y$ is divided by $7$ 

$x = 7$ $\displaystyle \times $$ a + 1 $   and  $y = 7 $ $\displaystyle \times $$ b + 2$

 $\displaystyle \therefore $ $ x + y = 7a + 7b + 1 + 2 = 7(a + b) + 3$

$\displaystyle \Rightarrow $$ (x + y)$ when divided by $7$ leaves a remainder $3$.

Prime factors of $140$ are :

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. ${2\times2\times 7}$

  2. ${2\times2\times5}$

  3. ${2\times2\times5\times7}$

  4. ${2\times2\times5\times7\times3}$

Show answer
Correct Option: C
Explanation:

Factors of $140$ are $1,140,7,20,2,70,4,35,5, 28,10,14$

Prime factors are $2, 7$ and $5.$
So, $140$ written as product of primes is $2\times 2 \times 5\times 7.$

The ........... when multiplied always give a new unique natural number.

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. decimal numbers

  2. fractions

  3. irrational numbers

  4. prime numbers

Show answer
Correct Option: D
Explanation:

For example: $24$ is made by multiplying the prime numbers $2, 2, 2$ and $3$ together. $24 = 2 \times 2 \times 2 \times 3$
It makes a unique number using a unique combination of $2, 2, 2$ and $3.$
Therefore, $D$ is the correct answer.

Fundamental theorem of arithmetic is also called as ______ Factorization Theorem.

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. Algebra

  2. Ambiguous

  3. Unique

  4. None of these

Show answer
Correct Option: C
Explanation:
$30 = 2 \times 3 \times 5$, where $2$ and $3$ are prime numbers.
We cannot get the number $30$ by multiplying any other prime numbers.
Example : $30 \neq 2 \times 5 \times 7.$ 
It is only with one particular set of prime numbers.
Hence, it is called Unique Factorization Theorem.
Therefore, $C$ is the correct answer.

We need blocks to build a building. In the same way _______ are basic blocks to form all natural numbers .

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. prime numbers

  2. real numbers

  3. unique numbers

  4. negative numbers

Show answer
Correct Option: A
Explanation:

Let us consider some examples.
$10 = 2 \times 5$, we need $2$ and $5$ which are prime numbers to get a new number $10$.
$12= 2 \times 2 \times 3$, we need $2$ and $3$ which are prime numbers to get a new number $12$.
Therefore$,$ $A$ is the correct answer.

................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. Pythagora's theorem

  2. Remainder theorem

  3. Fundamental theorem of arithmetic

  4. none of the above

Show answer
Correct Option: C
Explanation:

Fundamental theorem of arithmetic says that composite number can be factorised as a product of prime numbers.
Therefore, $C$ is the correct answer.

Fundamental theorem of arithmetic is basically used for ________

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. proving the irrationality of numbers.

  2. to explore when exactly the decimal expansion of a rational number is terminating or non-terminating repeating.

  3. prime numbers.

  4. both A and B.

Show answer
Correct Option: B
Explanation:

Fundamental theorem of arithmetic is basically used for firstly proving the irrationality of numbers and secondly to explore when exactly the decimal expansion of a rational number is terminating and when it is non - terminating repeating.
Therefore, $ B$ is the correct answer.

$2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. $1004$

  2. $828$

  3. $724$

  4. $936$

Show answer
Correct Option: D
Explanation:

$936 = 2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$
Therefore$, D$ is the correct answer.