Tag: maths

Questions Related to maths

If HCF of numbers $408$ and $1032$ can be expressed in the form of $1032x -408 \times 5$, then find the value of $x$.

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: C
Explanation:
$408=2\times2\times2\times3\times17$

$1032=2\times2\times2\times3\times43$

Hence, $HCF=2\times2\times2\times3=24$

Now, $1032x-408\times5=24\Rightarrow 1032x=2064\Rightarrow x=2$

Find the LCM and HCF of the following integers by the prime factorization mass

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. 12, 15 and 21

  2. 17, 23, and 29

  3. 8, 9 and 25

  4. 72 and 108

  5. 72 and 108

  6. 306 and 657

Show answer
Correct Option: A

The HCF of $420$ and $130$ is

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. $10$

  2. $15$

  3. $5$

  4. $3$

Show answer
Correct Option: A

The ratio of two numbers is 15:11. If their HCF be 13 then these numbers will be

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. 15, 11

  2. 75, 55

  3. 105, 77

  4. 195, 143

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Correct Option: A

Mark the correct alternative of the following.
The HCF of $100$ and $101$ is _________.

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. $1$

  2. $7$

  3. $37$

  4. None of these

Show answer
Correct Option: A
Explanation:

The given number $100$ and $101$ are consecutive numbers and respectively even and odd numbers.

So the HCF is $1$.

If HCF of $210$ and $55$ is of the form $(210) (5) + 55 y$, then the value of $y$ is :

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. $-19$

  2. $-18$

  3. $5$

  4. $55$

Show answer
Correct Option: A
Explanation:

  HCF of 210 and 55 is 5

Given HCF = $(210)(5)+55y$
$5 =(210)(5)+55y$
On solving this equation we get $y=-19$
 So correct answer will be option A

When the HCF of $468$ and $222$ is written in the form of  $ 468 x + 222y$ then the value of $ x$ and $y$ is 

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. $x =-9 \ and \ y =19$

  2. $x =9 \ and \ y = -19$

  3. $x =9\  and \ y = 19$

  4. $x =-9 \ and \ y =- 19$

Show answer
Correct Option: A
Explanation:

HCF of $468$ and $222$
$468 = \left(222 \times 2\right) + 24$
$222 = \left(24\times\ 9\right) + 6$
$24 = \left(6\times\ 4\right) + 0$
$\therefore HCF = 6$

$6 = 222 - \left(24\times\ 9\right)$
$ = 222 - \left[\left(468 -222 \times 2\right) \times\ 9\right]  $ [where $468 = 222 \times 2 + 24$]
$ = 222 - \left[468 \times 9 -222 \times 2 \times 9\right]$
$= 222 - \left(468 \times9\right) - \left(222\times 18\right)$
$ = 222 + \left(222 \times 18\right) - \left(468 \times9\right)$
$= 222\left[1 + 18\right]-  468 \times 9$
$= 222 \times19-  468 \times 9$
$  = 468 \times -9 + 222\times 19$
$\therefore x=-9$ and $y=19$.

If the H.C.F. of $A$ and $B$ is $24$ and that of $C$ and $D$ is $56,$ then the H.C.F. of $A, B, C$ and $D$ is

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. $4$

  2. $12$

  3. $8$

  4. $3$

Show answer
Correct Option: C
Explanation:

Given the H.C.F. of $A$ and $B$ is $24$ and that of $C$ and $D$ is $56.$
Then the H.C.F. of $A, B, C$ and $D$ is the HCF of $24$ and $56$ which is $8.$

The HCF of $136 ,170 \ and \ 255$ is 

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. $13$

  2. $15$

  3. $17$

  4. $1$

Show answer
Correct Option: C
Explanation:

136)170(1

  -    136
-------------------
          34)136(4
                136
----------------------------
                 0</div>

34)255(7
   -  238
-------------------
        17)34(2
             34
------------------------
              0

The H.C.F. of two expressions is x and their L.C.M is $ \displaystyle x^{3}-9x  $  IF one of the expression is $ \displaystyle x^{2}+3x  $  then,the other expression is 

maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

  1. $ \displaystyle x^{2}-3x $

  2. $ \displaystyle x^{3}-3x $

  3. $ \displaystyle x^{2}+9x $

  4. $ \displaystyle x^{2}-9x $

Show answer
Correct Option: A
Explanation:

Let two expressions $p(x)$ and $q(x)$ then

$p(x)\times q(x)=L.C.M.\ \times\ H.C.F.$

Since $p(x)=x^2+3x$
$(x^2+3x)\times q(x)=(x^3-9x) \times\ x$
$(x^2+3x)\times q(x)=(x^2-3x) \times\ (x^2+3x)$

$q(x)=(x^2-3x)$
Hence, this is the required solution.