Tag: common factors and hcf

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Questions Related to common factors and hcf

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

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

  1. $x =-9 \ and \ y =19$
  2. $x =9 \ and \ y = -19$
  3. $x =9\ and \ y = 19$
  4. $x =-9 \ and \ y =- 19$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $y=19$.

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

The HCF of $136 ,170 \ and \ 255$ is 

  1. $13$
  2. $15$
  3. $17$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

136)170(1

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

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

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

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 

  1. $ \displaystyle x^{2}-3x $
  2. $ \displaystyle x^{3}-3x $
  3. $ \displaystyle x^{2}+9x $
  4. $ \displaystyle x^{2}-9x $
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

The H.C.F. of the numbers $16.5, 0.90$ and $15$ is

  1. $16.5$
  2. $0.90$
  3. $15$
  4. $0.3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$1650 = 2\times 3\times 5^{2}\times 11$
$90 = 2\times 3^{2} \times 5^{1}$
$1500 = 2^{2} \times 3^{1} \times 5^{3}$
H.C.F. of $1650, 90$ and $1500$ is $2\times 3\times 5 = 30$

Therefore, H.C.F. of $16.5, 0.90$ and $15$ is $0.30$.
So, option D is correct.