Tag: real numbers on number line

Questions Related to real numbers on number line

HCF of the two numbers =

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

  1. Product of numbers + their LCM

  2. Product of numbers - their LCM

  3. Product of numbers $\times$ their LCM

  4. Product of numbers $\div$ their LCM

  5. Answer required

Show answer
Correct Option: D
Explanation:

The product of highest common factor $(H.C.F.)$ and lowest common multiple $(L.C.M.)$ of two numbers is equal to the product of two numbers.

If two numbers are $a$ and $b$ then
$HCF\ \times LCM=a\times b$ 

Hence,
$HCF=\dfrac{ab}{LCM}$

For example: 
Let $a=10\Rightarrow 2\times 5$ and $b=15\Rightarrow 3\times 5$
So, the $LCM$ of both numbers $=2\times 3\times 5\Rightarrow 30$
Then 
$HCF=\dfrac{10\times 15}{30}\Rightarrow 5$

Hence,
$HCF=\dfrac{Product\ of\ numbers}{Their\ LCM}.$

What is the HCF of $4x^{3} + 3x^{2}y - 9xy^{2} + 2y^{3}$ and $x^{2} + xy - 2y^{2}$?

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

  1. $x - 2y$

  2. $x - y$

  3. $(x + 2y)(x - y)$

  4. $(x - 2y)(x - y)$

Show answer
Correct Option: C
Explanation:

Let $f(x, y) = 4x^{2} + 3x^{2}y - 9xy^{2} + 2y^{3}$
and $g(x, y) = x^{2} + xy - 2y^{2}$
Clearly $(x - y) = 0$ or $x = y$ satisfy both equation, since for $x = y$ makes both equations zero. 

Hence, $(x - y)$ is the H.C.F. 
Similarly $(x + 2y) = 0$ i.e., $x = -2y$ also makes both equations zero. 
Thus, $(x + 2y)(x - y)$ is the H.C.F.

H.C.F. of $(10224, 1608)$ is _________.

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

  1. $12$

  2. $24$

  3. $48$

  4. $96$

Show answer
Correct Option: B
Explanation:

$10224 = 2^{4}\times3^{2}\times71$

$1608 = 2^{3}\times3\times67$

$\therefore$ H.C.F$(10224,1608) = 2^{3}\times3=24$

The greatest number that will divided $398, 436$ and $542$ leaving $7,11$ and $14$ remainders, respectively, is

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

  1. $16$

  2. $17$

  3. $18$

  4. $19$

Show answer
Correct Option: B
Explanation:

Out of tour choices only $17$ is the number that divides $398,436$ and $542$ leaving $7,11$ and $15$ as remainder

The smaller value of n for which $x^{2} - 2x - 3$ and $x^{3} - 2x^{2} - nx - 3$ have an H.C.F. involving $x$ is

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

The number of possible pairs of number, whose product is 5400 and the HCF is 30 is

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

  1. 1

  2. 2

  3. 3

  4. 4

Show answer
Correct Option: B
Explanation:

$ Given\quad that\quad product\quad of\quad the\quad number\quad is\quad 5400=30\times 3\times 2\times 30.\ \therefore \quad Possible\quad pairs\quad as\quad per\quad the\quad requirment\quad are-\ (1)\quad 30\times (3\times 2\times 30)=30\times 180\ (2)\quad (30\times 3)\times (2\times 30)=90\times 60\ \therefore \quad Total\quad number\quad of\quad pairs=2\quad \quad (Ans) $

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

Show answer
Correct Option: A