Tag: common factors and hcf

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

The H.C.F. of $\dfrac { 9 }{ 10 }$, $\dfrac { 12 }{ 25 }$, $\dfrac { 18 }{ 35 }$ and $\dfrac { 21 }{ 40 } $ is:

  1. $\dfrac { 3 }{ 5 } $
  2. $\dfrac { 252 }{ 5 } $
  3. $\dfrac { 3 }{ 1400 } $
  4. $\dfrac { 63 }{ 700 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Required H.C.F. $=\dfrac { H.C.F.\quad of\quad 9,12,18,21 }{ L.C.M.\quad of\quad 10,25,35,40 } = \dfrac { 3 }{ 1400 } $

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

What is the HCF of $3.0, 1.2$ and $0.06$?

  1. $0.6$
  2. $0.06$
  3. $6.0$
  4. $6.06$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given terms are $\dfrac {3}{1}, \dfrac {6}{5}$ and $\dfrac {3}{50}$.
H.C.F. of these terms $= \dfrac {\text{H.C.F. of}\ 3, 6, 3}{\text{L.C.M. of}\ 1, 5, 50}$
$= \dfrac {3}{50} = 0.06$

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

What is the HCF of the polynomials $x^{4} - 3x + 2, x^{3} - 3x^{2} + 3x - 1$ and $x^{4} - 1$?

  1. $x - 1$
  2. $x + 2$
  3. $x^{2} - 1$

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

$x^{4} - 3x + 2 = x^{4} - x^{3} + x^{3} - x^{2} + x^{2} - x - 2x + 2$
$= x^{3} (x - 1) + x^{2} (x - 1) + x(x - 1) - 2(x - 1)$
$= (x - 1) [x^{3} + x^{2} + x - 2]$
$x^{3} - 3x^{2} + 3x - 1 = (x - 1)^{3}$
$x^{4} - 1 = (x - 1) (x + 1) (x^{2} + 1)$
$HCF = x - 1$

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

Find $HCF$ by finding factors:
$16$ and $56$.

  1. $6$
  2. $18$
  3. $8$
  4. $9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Factorization of the following.
$16 = 2 \times 2 \times 2 \times 2$
$56 = 2 \times 2 \times 2 \times 7$
Since, the common factor is $2,2,8$,this implies that
$H.C.F = 2 \times 2 \times 2$
           $=8$
Hence,the correct option $C$.
Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find HCF by using prime factor method:
$54, 81$ and $99$.

  1. $8$
  2. $9$
  3. $10$
  4. $11$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Factorization of the following.
$54 = 2 \times 3 \times 3 \times 3$
$81 = 3 \times 3 \times 3 \times 3$
$99 = 3 \times 3 \times 11$
Since, the common factor is $3 \times 3$,this implies that
$H.C.F = 3 \times 3$
Hence,the correct option $B$.

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

Find $HCF$ by finding factors:
$75, 79$ and $89$.

  1. $2$
  2. $3$
  3. $1$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Factorization of the following 
$75 = 5 \times 5 \times 3\times 1$
$79=1 \times 79$
$89 = 1 \times 89$
Since, the common factor is $1$ this implies that
$HCF = 1$

Hence, the correct option is $C$

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

Manukaka distribute $96$ marbles among the children of a class in such a way that each child got equal number of marble. In the same class, sameway he also distributed $72$ chocolates. No chocolate and marble is left. How many maximum students are there in this class so that it is possible?

  1. $22$
  2. $24$
  3. $26$
  4. $28$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Factorization of the following.
Maximum students are $ =24$
$72 = (1,2,3,4,6,8,9,12,72)$
$24 = (1,2,3,4,6,8,12,24)$
Since, The common factor is $1,2,3,4$
$H.C.F = 24$
Hence, The correct option is $B$
Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find HCF by using prime factor method:
$66$ and $88$.

  1. $21$
  2. $23$
  3. $24$
  4. $22$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Factorization of the following

$66 = 1 \times 3 \times 2 \times 11$
$88 = 1 \times 2 \times 2 \times 2 \times 11$
Since, the common factor is $1,2,11$ this implies that 
$HCF=22$
Hince, the correct option $D$