Tag: hcf-lcm

Questions Related to hcf-lcm

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

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

  1. $4(x-2)$

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

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

  4. None of these

Show answer
Correct Option: A
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.

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

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

  1. $3^5$

  2. $3^9$

  3. $3^{14}$

  4. $3^{28}$

Show answer
Correct Option: A
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

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

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

  1. $243$

  2. $189$

  3. $113$

  4. $297$

Show answer
Correct Option: D
Explanation:

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

The greatest number that will divide 37, 50, 123 leaving remainder 1, 2 and 3 respectively is

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

  1. 9

  2. 10

  3. 15

  4. 12

Show answer
Correct Option: D
Explanation:

$37-1=36, 50-2=48$
$123-3=120$
HCF of 36, 48 and $120=12$
$\therefore$ required number $=12$.

What is the H.C.F. of 1134, 1344 and 1512?

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

  1. $42$

  2. $64$

  3. $1344$

  4. $1512$

Show answer
Correct Option: A
Explanation:

$1134 = 2\times3^{4}\times7$


$1344 = 2^{6}\times3\times7$


$1512 = 2^{3}\times3^{3}\times7$


$\therefore$ H.C.F $= 2\times 3\times 7 = 42$

HCF of $10$ and $100$ is

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

  1. $10$

  2. $100$

  3. $5$

  4. All of the above

Show answer
Correct Option: A
Explanation:

$10=5\times 2$
$100=5\times 2\times 5\times 2=5^2\times 2^2$
$HCF = 5\times 2=10$

So, option $A$ is correct.

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

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

  1. $5$

  2. $9$

  3. $15$

  4. $25$

  5. $45$

Show answer
Correct Option: E
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

Find the greatest common factor of $42,126$ and $210$.

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

  1. $2$

  2. $6$

  3. $14$

  4. $21$

  5. $42$

Show answer
Correct Option: E
Explanation:

We know, $42=2\times 3\times 7$

$126=2\times 3\times 3\times 7$
$210=2\times 3\times 5\times 7$
$\therefore$ H.C.F $=2\times 3\times 7=42$

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

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

  5. More than $4$

Show answer
Correct Option: D
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 $42$.

Which of the following is a factor of 60?

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

  1. $18$

  2. $25$

  3. $30$

  4. $35$

  5. $45$

Show answer
Correct Option: C
Explanation:

In the given answers $30$ is a factor of $60$, as factors of $60$ are
$2,3,4,5,6,10,12,15,30,20,60$