Tag: common factors and hcf

Questions Related to common factors and hcf

Greatest number which divided $926$ and $2313$, leaving $2$ and $3$ remainders, respectively, is?

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

  1. $462$

  2. $54$

  3. $152$

  4. $154$

Show answer
Correct Option: A
Explanation:

A number divides 926 and 2313 leaving remainders 2 and 3 respectively.

This means that the number perfectly divides 926 - 2 = 924 as well as 2313 - 3 = 2310.

Now we simply need to find the HCF of 924 and 2310 

On calculating the HCF , we get it as  462

Hence, the answer is 462

Choose the correct answer from the alternatives given.
LCM of $\dfrac 14 $and $\dfrac 18$ is

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

  1. $\dfrac12$

  2. $1$

  3. $\dfrac 14$

  4. $\dfrac 18$

Show answer
Correct Option: C
Explanation:
We know that,
LCM of dfrac tions = $\dfrac { LCM\ of\ numerators}{HCF\ of\ denominators}$
= $\dfrac { LCM (1,1)}{ HCF(4,8)} = \dfrac {1}{4}$ 

The greatest integer that divides 358, 376, 334 leaving the same remainder in each case is

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

  1. 6

  2. 7

  3. 8

  4. 9

Show answer
Correct Option: A
Explanation:

The difference between each set of two numbers is respectively 18, 42 and 24.
Now, as the remainder should be the same in each case, the number is the greatest common divisor of 18, 24 and 42.
$18=2\times 3\times 3$
$24=2\times 2\times 2\times 3$
$42=2\times 3\times 7$
$\therefore HCF=2\times 3=6$
$\therefore$ The required number is 6.

A merchant has $120$ litres of oil of one kind, $180$ litres  of another kind and $240$ litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?

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

  1. $20$ liters

  2. $30$ liters

  3. $60$ liters

  4. $80$ liters

Show answer
Correct Option: C
Explanation:
$\text{We need to find the HCF or GCD that is Greatest Common Divisor}$ 

${120 = 2^3 \times3\times5}$

${180 = 2^2\times3^2 \times5}$

${240 = 2^4\times3\times5}$

${GCD = 2^2\times3\times5= 60}$

$\text{The greatest capacity = 60 liters}$

$\text{So the merchant needs to fill 60 liters of all types of oils }$

$\text{Hence option C is correct}$


HCF of two co-prime numbers is ___.

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

  1. $1$

  2. $0$

  3. $2$

  4. None of the above

Show answer
Correct Option: A
Explanation:

When two numbers have no common factors other than $1$, so they are co-prime numbers.

So, their HCF is $1$.
Hence, the answer is $1$.

HCF of $36$ and $144$ is ______.

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

  1. $36$

  2. $144$

  3. $4$

  4. $2$

Show answer
Correct Option: A
Explanation:

To find the HCF of $36$ and $ 144 $, first factorise them:

$36= 2 \times 2 \times 3 \times 3 $
$144= 2 \times 2 \times 2 \times 3 \times 3 $
Taking common factor, we get

HCF $= 2 \times 2 \times 3 \times 3 $ $=36$

Hence, the answer is $36$.