Question

A book seller has 28 Kannada and 72 English books. The books are of the same size. These books are to be packed in separate bundles and each bundle must contain the same number of books. Find the least number of bundles which can be made and also the number of books in each bundle.

Answer 1

Hint: First, we have to understand what we are asked to find, and we will get this by using the concept of Highest common factor (HCF). We will find HCF by using the prime factorization method. After finding HCF of 72,28 that value will be answer of each bundle and dividing 72,28 by that number will get each number of books i.e. Kannada and English.

Complete step by step answer:
Here, we will understand the definition of Highest common factor (HCF).
The largest number that divides two or more numbers is the highest common factor (HCF) for those numbers. Let us consider the numbers say $30\left( 2\times 3\times 5 \right),36\left( 2\times 2\times 3\times 3 \right)$ then here, number 2 is there one time in the factor and number 3 is there one time in factors. So, HCF will be $2\times 3=6$ .
Similarly, we will find HCF of 72 and 28. We will get as
$28=2\times 2\times 7$
$72=2\times 2\times 2\times 3\times 3$
Here, we can see that in 28 i.e. number 2 is repeated twice and is also repeated twice in 72. Rest number 7 and number 3 are not repeated in both 28, 72.
So, HCF of 72, 28 is $2\times 2=4$ .
Thus, the number of bundles will be 4.
Now, to find each bundle contains how many books can be obtained by dividing 72, 28 by HCF. On solving we get as
$\dfrac{72}{4}=18$ and $\dfrac{28}{4}=7$
Thus, there are 7 books of Kannada and 18 books of English in each bundle.

Note: Be careful in this type of problem. Sometimes mistakes happen in not understanding whether to take LCM or HCF and instead of HCF, taking LCM then the answer will be totally different and at last it will be wrong. Now, if LCM is taken then LCM of 72 and 28 will be $28=2\times 2\times 7$ , $72=2\times 2\times 2\times 3\times 3$ . On solving we get $2\times 2\times 2\times 3\times 3\times 7=504$ . So, there will be at least 504 bundles and a number of books will be in decimal form i.e. $\dfrac{72}{504}$ and $\dfrac{28}{504}$ . This is totally wrong so, do not make this mistake.