Answer
424.5k+ views
Hint: This question talks about the number of soaps in each box can be packed so that number of boxes is the least ,so for this we have to find HCF (HIGHEST COMMON FACTOR) of both numbers and the HCF is our answer. HCF can be find by using two method
1. By using Euclid’s division algorithm
2. by using prime factorization method
Complete step-by-step answer:
We used HCF to find the answer because in the question it is given that the entire box contains only one kind of soap and the box must be full. As the name suggests the highest common factor is the largest number which divides both the given number. We considered the largest number because in the question it is given that we have to make as many less boxes as possible.
According to the question we have 612 dettol soaps and 342 pear soaps and we have to find the maximum number of soaps in each box.
To find the maximum number of soaps in each box we take HCF (HIGHEST COMMON FACTOR) of 612 and 342.
By using Euclid’s division algorithm, we have
$612 = 342 \times 1 + 270$
$342 = 270 \times 1 + 72$
$270 = 72 \times 3 + 54$
$72 = 54 \times 1 + 18$
$54 = 18 \times 3 + 0$
Here we notice that the remainder is zero, and the divisor at this stage is 18. Therefore HCF of 612 and 342 is 18.
So, the trader can pack 18 soaps per box.
Note: alternative method for this question
We can find HCF by prime factorization method where we have to write prime factor of \[612\] and $342$
So prime factor of $612$ is
$612 = 2 \times 2 \times 3 \times 3 \times 17$
And prime factor of $342$ is
$342 = 2 \times 3 \times 3 \times 19$
Now for HCF we have to collect common factor so we can see 2 ,3,3 are common factor
So HCF ($612,342$) = $2 \times 3 \times 3$
HCF ($612,342$) = $18$
So find the maximum number of soaps in each box = 18
1. By using Euclid’s division algorithm
2. by using prime factorization method
Complete step-by-step answer:
We used HCF to find the answer because in the question it is given that the entire box contains only one kind of soap and the box must be full. As the name suggests the highest common factor is the largest number which divides both the given number. We considered the largest number because in the question it is given that we have to make as many less boxes as possible.
According to the question we have 612 dettol soaps and 342 pear soaps and we have to find the maximum number of soaps in each box.
To find the maximum number of soaps in each box we take HCF (HIGHEST COMMON FACTOR) of 612 and 342.
By using Euclid’s division algorithm, we have
$612 = 342 \times 1 + 270$
$342 = 270 \times 1 + 72$
$270 = 72 \times 3 + 54$
$72 = 54 \times 1 + 18$
$54 = 18 \times 3 + 0$
Here we notice that the remainder is zero, and the divisor at this stage is 18. Therefore HCF of 612 and 342 is 18.
So, the trader can pack 18 soaps per box.
Note: alternative method for this question
We can find HCF by prime factorization method where we have to write prime factor of \[612\] and $342$
So prime factor of $612$ is
$612 = 2 \times 2 \times 3 \times 3 \times 17$
And prime factor of $342$ is
$342 = 2 \times 3 \times 3 \times 19$
Now for HCF we have to collect common factor so we can see 2 ,3,3 are common factor
So HCF ($612,342$) = $2 \times 3 \times 3$
HCF ($612,342$) = $18$
So find the maximum number of soaps in each box = 18
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)