Tag: common factors and hcf

Questions Related to common factors and hcf

Find the greatest number which divides 120, 165 and 210 exactly leaving remainders 5, 4 and 3 respectively

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

  1. 7

  2. 5

  3. 23

  4. None of these

Show answer
Correct Option: D
Explanation:

The required number will be the H.C.F of (120 - 5), (165 - 4) and (210 - 3) i.e. H.C.F. of 115
161 and 207
$\displaystyle \therefore $ Required number = H.C.F. of 115, 161 and 207 = 23

HCF of $24, 36$ and $92$ is:

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

  1. $24$

  2. $36$

  3. $12$

  4. $4$

Show answer
Correct Option: D
Explanation:

The HCF of $24,36,92$ can be found by factorising all three numbers:

$24= 2 \times 2 \times 2 \times 3 $
$36= 2 \times 2 \times 3 \times 3 $
$92 =2 \times 2 \times 23 $
Now, common factors are $2$ and $2$
So, HCF is $ 2 \times 2=4$
Hence, the answer is $4$.

The HCF of $18$ and $30$ is equal to

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

  1. $6$

  2. $5$

  3. $4$

  4. $3$

Show answer
Correct Option: A
Explanation:

$18 = 2 \times 3 \times 3$

$30 = 2 \times 3 \times 5$
So, H.C.F of $18$ and $30$ is $6$.
So, option A is correct.

The HCF of $75$ and $15$ is equal to

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

  1. $12$

  2. $13$

  3. $14$

  4. $15$

Show answer
Correct Option: D
Explanation:

$75=5^2\times 3$

$15=5\times3$
HCF$=15$

What is the least number by which $825$ must be multiplied in order to produce a multiple of $715 ?$

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

  1. $13$

  2. $15$

  3. $11$

  4. $3$

Show answer
Correct Option: A
Explanation:

$825=3\times5\times5\times 11$

$715=5\times11\times13$
In the factor of both numbers, $13$ is not common. 
Hence, the least number by which $825$ must be multiplied in order to produce a multiple of $715=13.$

The the H.C.F of $420$ and $396$ is equal to

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

  1. $12$

  2. $13$

  3. $14$

  4. $15$

Show answer
Correct Option: A
Explanation:

$420 =7 \times 5\times 3\times 2^2$
$396=2^2 \times 3^2\times 11$
So, $H.C.F=2^2 \times 3$
Ans- Option $A$

The HCF of $12$ and $24$ is equal to

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

  1. $6$

  2. $12$

  3. $24$

  4. None of the above

Show answer
Correct Option: B
Explanation:

$12 = 2 \times 2 \times 3 $

$24 = 2 \times 2 \times 2 \times 3$ 
So, HCF of $12$ and $24$ is $12$.
So, option B is correct.

The HCF of $75$ and $180$ is equal to

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

  1. $11$

  2. $12$

  3. $13$

  4. $15$

Show answer
Correct Option: D
Explanation:
$180=60 \times 3 =5\times2^2\times 3^2$
$75=5^2 \times 3$
HCF$=15$

Find the G.C.F of $2541$ and $3102$ in the scale of seven.

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

  1. $87$

  2. $54$

  3. $33$

  4. $85$

Show answer
Correct Option: C
Explanation:
Prime factors of $2541$ are $3, 7, 11, 11$. Prime factorization of $3102$ in exponential form is

$2541=3^1\times 7^1\times 11^2$


Prime factors of $3102$ are $2, 3, 11, 47$. Prime factorization of $3102$ in exponential form is

$3102=2^1\times 3^1\times 11^1\times 47^1$

We found the factors and prime factorization of $2541$ and $3102$. The biggest common factor number is the $GCF$ number.


So, the greatest common factor $2541$ and $3102$ is $3\times 11=33$.

Hence, this is the answer.

Find $HCF$ by finding factors:
$6$ and $8$.

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

  1. $4$

  2. $6$

  3. $2$

  4. $8$

Show answer
Correct Option: C
Explanation:

Factorization of the following.

$6 = 3 \times 2\times 1$
$8 = 2 \times 2 \times 8\times 1$

Since, The common factor is $2$.This implies that
$H.C.F = 2$

Hence,the correct option is $C$