A book seller has 420 science books and 130 English books. He want to stack them in such a way that each stack has the same number and they take up the last area of the surface. What is the maximum number of Science books that can be placed each stack of this purpose ?
Answers
Answer:
(i) Maximum number of books : 10 books
(ii) Mathematical concept used : H.C.F - Highest Common Factor.
To find :
(i) Maximum number of books.
(ii) Mathematical concept used.
Given :
A book seller has 2 stream books.
They are :
(1) 420 Science stream books.
(2) 130 Arts stream books.
(i) Maximum number of books :
Using the H.C.F methodology maximum number of books can be found.
H.C.F ( Science stream books, Arts stream books ) = H.C.F ( 420, 130 )
H.C.F of 420 :
By factorizing we get,
H.C.F of 420 = 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 .
H.C.F of 130 :
By factorizing we get,
H.C.F of 130 = 1, 2, 5, 10, 13, 26, 65, 130.
So, the H.C.F ( 420, 130 ) is 10.
Hence, the maximum number of books is 10 books that can be placed in each stack.
(ii) Mathematical concept used :
H.C.F :
H.C.F stands for Highest Common Factor.
It is also known as Greatest common Factor (G.C.F).
Steps to find H.C.F given below :
When the data is given,
(a) Factorize the given number.
(b) Search for common numbers.
(c) Select highest or greatest common number.
For example,
Find H.C.F of 12 and 16.
Given :
H.C.F ( 12, 16 )
(a) Factorize the given number :
H.C.F of 12 = 1, 2, 3, 4, 6, 12.
H.C.F of 16 = 1, 2, 4, 8, 16.
(b) Search for common numbers :
Common numbers in H.C.F of 12 = 1, 2, 4.
Common numbers in H.C.F of 16 = 1, 2, 4.
(c) Select highest or greatest common number :
Highest common factor in H.C.F of 12 and 16 is 4.
Answer:
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