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REAL NUMBERS
 Find the largest positive integer that will divide
122,150 and 115 leaving remainder 5,7 & 11 respectively.
Solution 1: 122-5 = 117 is exactly divisible by the required
number
150-7 = 143,
115-11 = 104
So, required number is the HCF of 117,143,104
117 = 3x3x13
143 = 11x13
104 = 2x2x2x13
HCF ( 117,143,104 ) = 13
Hence, required number is 13.
 Use Euclid’s division algorithm to find the largest
number which divides 957 and 1280 leaving remainder 5 in
each case.
Solution 2: 957-5=952 and 1280-5= 1275,are completely
divisible by required number.Now find the HCF by Euclid
division lemma,
1275 > 952 by apply division lemma
1275 = 952 x 1 + 323 ( since R? 0 )
952 = 323 x 2 + 306
( since R? 0 )
323 = 306 x 1 + 17
( since R ? 0)
306 = 17 x 18 + 0
here R = 0
Divisor in the last step is 17
HCF of 1275 and 952 is 17.
Hence required number is 17.
 In a school there are two sections of class 10th.there
are 40 students in 1st section and 48 students in
second section. Determine the minimum number of books
required for their class library so that they can be
distributed equally among students of both sections.
Solution 1: Required number of books = LCM ( 40,48 )
40 = 2x2x2x5
48 = 2x2x2x2x3
LCM (40,48) = 2x2x2x2x3x5 = 240
Hence, required number of books are 240
 In a morning walk Nirmaljeet, Puneet, Rajiv step off
together, their steps measuring 240 cm , 90 cm, 120cm
respectively. What is the minimum distance each should
walk so that one can cover the distance in complete
steps?
Solution 2:
240 = 2x2x2x2x3x5
90 = 2x3x3x5
120 = 2x2x2x3x5
LCM = 2x2x2x2x3x3x5 = 720
Hence required distance 720 cm.
 The sets of mathematics, physics and physical education
books have to be stacked in such a way that all the
books are stored topic wise. The number of mathematics ,
physics and physical education books are 14 , 18 and 22.
Determine the number of stacks of each books provided
books are of the same thickness.
Solution 3:
condition,
Firstly , to arrange the books as according to
Find HCF of 14, 18 and 22.
14 = 2x7
18 = 2x3x3
22 = 2x11
HCF = 2
So ,there are only 2 books in each stack.
Number of stack of Mathematics books =
= 7
Number of stack of Physics books = = 9
Number of stack of Physical Education books =
= 11.