Tag: hcf

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Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find G.C.D of: $(x^2-9)(x-3)$ and $x^2+6x+9$

  1. $(x+3)^2$

  2. (x-3)

  3. (x+3)

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$p(x) = (x^2-9)(x-3)$
        $= (x^2-3^2)(x-3)$
        $= (x-3)(x+3)(x-3)$
and
$q(x) = x^2+6x+9$
        $ = x^2+3x+3x+9$
        $ = x(x+3)+3(x+3)$
        $= (x+3)(x+3) $
$\therefore $ G.C.D of $p(x)$ and $q(x) = x+3 $
Option C is correct.

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find G.C.D of: $8(x^4-16)$ and $12(x^3-8)$

  1. $4(x-2)$
  2. $3(x^3-8)$
  3. $2(x^2-4)$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$p(x) =8(x^4-16)$
   $= 4\times 2 [(x^2)^2 - 4^2] $
   $ = 4\times 2 (x^2 - 4) (x^2 + 4) $
   $ = 4\times 2  (x+2)(x-2) (x^2 +4) $
and
 $q(x) = 12(x^3-8)$
       $=4\times 3 (x^3 - 2^3) $
         $=4\times 3 (x - 2)(x^2 + 2x + 4) $
$\therefore $ G.C.D of $p(x)$ and $q(x) = 4(x-2) $
Option A is correct.

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The HCF of $3^5$, $3^9$, and $3^{14}$ is

  1. $3^5$
  2. $3^9$
  3. $3^{14}$
  4. $3^{28}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

${ 3 }^{ 5 }$ = 3x3x3x3x3

${ 3 }^{ 9 }$ = 3x3x3x3x3x3x3x3x3
${ 3 }^{ 14 }$ = 3x3x3x3x3x3x3x3x3x3x3x3x3x3x3
Common factors are 3x3x3x3x3
SO HCF will be ${ 3 }^{ 5 }$
Correct answer will be option A

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The GCD and LCM of two numbers a and b are, respectively, 27 and 2079. If a is divided by 9, the quotient is 21. Then b is

  1. $243$
  2. $189$
  3. $113$
  4. $297$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the two numbers be $a$ and $b$.
$a=quotient\times dividend$
$a=21\times 9$
  $=189$
$\therefore b=\frac { GCD\times LCM }{ a }$
                  $=\frac { 27\times 2079 }{ 189 }$
                  $=297$

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

What is the greatest common factor of $45,135$ and $270$?

  1. $5$
  2. $9$
  3. $15$
  4. $25$
  5. $45$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The factors of the given numbers are :
$45  = 1,3,5,9,15$ and $45$
$135 = 1,3,5,9,15,45$ and $135$
$270 = 1,3,5,9,15,45,90,135$ and $270$
The common factors in each of the above numbers are $3,3$ and $5$.
Hence, the GCF is $3\times 3\times 5$ = 45
and as $45$ is also a factor of both $135$ and $270$.
The GCF of $45, 135$ and $270$ is $45$.
The correct answer is Option E, the number $45$.

Ans: E

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

How many different positive integers are factors of both $28$ and $42$?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. More than $4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$4$ positive integers are factors of $28$ and $42$ both.
For example,
$1,4, 7, 6$ and $28$ itself is a factor of $28$.
$1,4, 7, 6$ and $42$ itself is factor of $42$.