Tag: maths

Questions Related to maths

The HCF of the numbers $0.48, 0.72$ and $0.108$  is

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

  1. $1$

  2. $12$

  3. $0.12$

  4. $0.012$

Show answer
Correct Option: D
Explanation:

$480=2^5\times 3\times 5$
$720=2^4\times 3^2\times 5$
$108=2^2\times 3^2$
$HCF=2^2\times 3=12$

HCF of $0.48, 0.72$ and $0.108 = 0.012$
So, option $D$ is correct.

The the HCF of $248$ and $492$ is equal to

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

  1. $2$

  2. $3$

  3. $4$

  4. $5$

Show answer
Correct Option: C
Explanation:

$248=2^3 \times 31$

$492=2^2 \times 3 \times 41$
HCF is $4.$

Find the HCF of $26$ and $455$

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

  1. $11$

  2. $12$

  3. $13$

  4. none of the above

Show answer
Correct Option: C
Explanation:

$26=13\times 2$

$455=5\times 13\times 7$
HCF is $13.$

The H.C.F. of the numbers $16.5, 0.90$ and $15$ is

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

  1. $16.5$

  2. $0.90$

  3. $15$

  4. $0.3$

Show answer
Correct Option: D
Explanation:

$1650 = 2\times 3\times 5^{2}\times 11$
$90 = 2\times 3^{2} \times 5^{1}$
$1500 = 2^{2} \times 3^{1} \times 5^{3}$
H.C.F. of $1650, 90$ and $1500$ is $2\times 3\times 5 = 30$

Therefore, H.C.F. of $16.5, 0.90$ and $15$ is $0.30$.
So, option D is correct.

The HCF of two consecutive even numbers is

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

  1. $6$

  2. $3$

  3. $4$

  4. $2$

Show answer
Correct Option: D
Explanation:

$HCF$ of two consecutive even numbers is always $2$. For example:


$HCF$ of $2$ and $4$ is $2$ and similarly,

$HCF$ of $22$ and $24$ is $2$ and we can do so on..

The HCF of two consecutive odd numbers is

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

  1. $28$

  2. $30$

  3. $1$

  4. $5$

Show answer
Correct Option: C
Explanation:


Let's take two odd numbers $15$ and $17$.
Factors of $15 = 1, 3, 5$
Factors of $17 = 1, 17$
HCF is $1$
Therefore, $C$ is the correct answer.
OR
HCF of $25$ and $27$ is also $1$

There are five odd numbers $1, 3, 5, 7, 9$. What is the HCF of these odd numbers?

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

  1. $2$

  2. $1$

  3. $6$

  4. $5$

Show answer
Correct Option: B
Explanation:
$3=3 \times 1$
$5=5 \times 1$
$7=7 \times 1$
$9=3 \times 3$
HCF is $1$ for the five odd numbers.
Therefore, $B$ is the correct answer.

Find HCF of $70$ and $245$ using Fundamental Theorem of Arithmetic. 

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

  1. $35$

  2. $30$

  3. $15$

  4. $25$

Show answer
Correct Option: A
Explanation:
using Fundamental Theorem of Arithmetic
$70 =2\times 5\times 7$
$245=5\times 7 \times 7 $
Common factors of 70 and 245 are 5 and 7.
$\therefore HCF = 5\times 7=35$
hence, option $A$ is correct.

Three ropes are $7\ m, 12\ m\ 95\ cm$ and $3\ m\ 85\ cm$ long. What is the greatest possible length that can be used to measure these ropes?

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

  1. $35\ cm$

  2. $55\ cm$

  3. $1\ m$

  4. $65\ cm$

Show answer
Correct Option: A
Explanation:

The given three ropes are $7$m, $12$ m $95$cm and $3$m$85$cm long. We know that $1$m=$100$cm, therefore,


The length of the respective ropes will be:

1st rope $=7\times 100=700$cm
2nd rope $=(12\times 100)+95=1200+95=1295$cm
3rd rope $=(3\times 100)+85=300+85=385$cm

Now, let us factorize the length of the ropes as follows:

$700=2\times 2\times 5\times 5\times 7\ 1295=5\times 7\times 37\ 385=5\times 7\times 11$

The highest common factor (HCF) is $5\times 7=35$

Hence, the greatest possible length that can be used to measure these ropes is $35$cm.

H.C.F. of $26$ and $91$ is:

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

  1. $13$

  2. $2366$

  3. $91$

  4. $182$

Show answer
Correct Option: A
Explanation:

$26=2*13$
$91=7*13$
$HCF=13$
As it is the only common factor