Tag: hcf-lcm

Questions Related to hcf-lcm

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?

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

  1. $22$

  2. $24$

  3. $26$

  4. $28$

Show answer
Correct Option: B
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 $B$

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

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

  1. $21$

  2. $23$

  3. $24$

  4. $22$

Show answer
Correct Option: D
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 $D$

Find HCF by using prime factor method:
$25$ and $55$.

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

  1. $5$

  2. $3$

  3. $2$

  4. $4$

Show answer
Correct Option: A
Explanation:

Factorization of the following

$25 = 1 \times 5 \times 5$
$55 = 1 \times 5 \times 11$
Since. the common factor is $1,5$ this implies that 
$HCF=5$
Hence, the correct option $A$

What is the HCF of $13$ and $22$?

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

  1. $13$

  2. $22$

  3. $1$

  4. $286$

Show answer
Correct Option: C
Explanation:
Factorization of the following.
HCF=Highest common factor
 so  HCF between $\left( {13,22} \right)$
$ \Rightarrow 13 = 1,13\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - eq.\left( 1 \right)$
$ \Rightarrow 22 = 1,2,11,22\,\,\,\,\,\,\,\,\,\,\, - eq.\left( 2 \right)$  
$(1)$ &$(2)$ equation common is $1$.
Since, The common factor is $1$. This implies that
 then HCF  is $1$.
Hence, the correct option is $C$.

G.C.D of $4$ and $19$ is _________.

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

  1. $1$

  2. $4$

  3. $19$

  4. $76$

Show answer
Correct Option: A
Explanation:

There is no common factor between $4$ and $19$. Hence, G.C.D. of $4$ and $19$ is $1$.

The two numbers nearest to 10000 which are exactly divisible by each of 2, 3, 4, 5, 6 and 7, are _____.

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

  1. 9660, 10080

  2. 9320, 10080

  3. 9660, 10060

  4. 10340, 10080

Show answer
Correct Option: A
Explanation:

The numbers which are exactly divisible by 2, 3, 4, 5, 6 and 7 are the multiples of the LCM of the given numbers.
$\therefore$  LCM = 2 x 2 x 3 x 5 x 7 = 420
Now, dividing 10000 by 420, we get remainder = 340
$\therefore$  Number just less than 10000 and exactly divisible by the given numbers = 10000 - 340 = 9660
Number just greater than 10000 and exactly divisible by the given numbers = 10000 + (420 - 340) = 10080

If the HCF of 85 and 153 is expressible in the form $85n -153$, then the value of n is:

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

  1. 3

  2. 2

  3. 4

  4. 1

Show answer
Correct Option: B
Explanation:

$85 = 5 \times  17$

$153 = 3 \times  3 \times 17$
So HCF will be 17
$17 = 85n-153$ from here we get n=2
So the correct answer is option B

If the HCF of 85 and 153 is expressible in the form 85n $-$ 153, then value of n is :

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

  1. 3

  2. 2

  3. 4

  4. 1

Show answer
Correct Option: B
Explanation:

HCF of $85\  and\  153 = 17$

Now given HCf can be expressed in the gorm of $85n-153$
So $17=85n-173$
On solving the above equation we get $n=2$
So correct answer will be option B

Choose the correct answer form the alternatives given.
What is the HCF of $(x^4 \, - \, x^2 \, - \, 6) \, and \, (x^4 \, - \, 4x^2 \, + \, 3)$? 

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

  1. $x^2$ - $3$

  2. $x + 2$

  3. $x + 3$

  4. $x^2$ + $3$

Show answer
Correct Option: A
Explanation:

$\displaystyle (x^4 \, - \, x^2 \, - \, 6) \, = \, (x^2 \, - \, 3) (x^2 \, + \, 2)$
$\displaystyle (x^4 \, - \, 4x^2 \, + \, 3) \, = \, (x^2 \, - \, 3) (x^2 \, - \, 1)$
HCF is = $x^2$ - $3$

The greatest common divisor of $878787878787$ and $787878787878$ equals.

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

  1. $3$

  2. $9$

  3. $27$

  4. $101010101010$

  5. $303030303030$

Show answer
Correct Option: E
Explanation:

$787878787878)878787878787(1\ \quad \quad \quad \quad \quad  -\underline { 787878787878 } \ \quad \quad \quad \quad \quad \quad \quad 90909090909)787878787878(8\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad  \underline { -727272727272 } \ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad 60606060606)90909090909(1\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \underline { -60606060606 } \ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad 30303030303)60606060606(2\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \underline { -60606060606 } \ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad  \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad 0$

$\therefore$ G.D.C = 30303030303