Tag: common factors and hcf

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

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

  1. $462$
  2. $54$
  3. $152$
  4. $154$
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

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

  1. $\dfrac12$
  2. $1$
  3. $\dfrac 14$
  4. $\dfrac 18$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We know that,
LCM of dfrac tions = $\dfrac { LCM\ of\ numerators}{HCF\ of\ denominators}$
= $\dfrac { LCM (1,1)}{ HCF(4,8)} = \dfrac {1}{4}$ 
Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

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

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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?

  1. $20$ liters
  2. $30$ liters
  3. $60$ liters
  4. $80$ liters
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$\text{We need to find the HCF or GCD that is Greatest Common Divisor}$ 

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

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

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

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

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

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

$\text{Hence option C is correct}$


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

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

  1. $36$
  2. $144$
  3. $4$
  4. $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $36$.