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SSC Real Numbers Exercise - 1.2 of 10th class


Class 10 Real Numbers Exercise 1.2

SSC Real Numbers :


  • Positive or negative, Large or small, whole numbers or decimal numbers are all Real Numbers. 

They are called “Real Numbers” because they are not Imaginary Numbers.





Class 10 Real Numbers Exercise 1.2

EXERCISE – 1.2


1Q.  Express each of the following number as a product of its prime factors.


i)      140         ii) 156              iii) 3825                     iv) 5005                   v) 7429


Sol 140



        140 = 2 X 2 X 5 X 7 = 22 X 5 X 7


 

Sol ii) 156









156 = 2 X 2 X 3 X 13 = 22 X 3 X 13




Sol :      iii)   3825


 









3825 = 3 X 3 X 5 X 5 X 17


= 32 X 52 X 17


Sol :      iv)   5005


 







πŸ‘‰ 5005 = 5 X 7 X 11 X 13


Sol :         v)   7429








πŸ‘‰ 7429 = 17 X 19 X 23


πŸ‘‰ CLICK HERE FOR REAL NUMBER EXERCISE 1.1 

πŸ‘‰ CLICK HERE FOR REAL NUMBER EXERCISE 1.3

πŸ‘‰ CLICK HERE FOR REAL NUMBER EXERCISE 1.4


SSC Real Numbers


2Q. Find the L.C.M and H.C.F of the following integers by the prime factorization method.


Sol. i) 12, 15 and 21                ii) 17, 23 and 29


iii) 8, 9 and 25                            iv) 72 and 108


 

Sol :      i) 12, 15 and 21


            12 = 2 X 2 X 3 = 22 X 3


            15 = 3 X 5


             21 = 3 X 7


   L.C.M = 22 X 3 X 5 X 7 = 420


   H.C.F = 3


Sol : ii) 17, 23 and 29


The given numbers 17, 23 and 29 are all primes.


L.C.M = their product


= 17 X 23 X 29 = 11339


H.C.F = 1


iii) 8, 9 and 25


            8 = 2 X 2 X 2 = 23


            9 = 3 X 3 = 32


             25 = 5 X 5 = 52


     L.C.M = 23 X 32 X 52 = 1800


                 ( OR )

8, 9 and 25 are relatively prime, there fore L.C.M is equal to their product. (i.e.) L.C.M = 8 X 9 X 25 = 1800


H.C.F = 1


iv) 72 and 108










72 = 2 X 2 X 2 X 3 X 3 

72 = 23 X 32













108 = 22 X 33


L.C.M = 23 X 33 = 8 X 27 = 216


H.C.F = 22 X 32 = 4 X 9 = 316


v)   306 and 657





 



306 = 2 X 32 X 17

657 = 32 X 73

L.C.M = 2 X 32 X 17 X 73 = 22338

H.C.F = 32 = 9.


SSC Real Numbers

Class 10 Real Numbers Exercise 1.2

3Q. Check whether 6n can end with the digit ‘0’ for any natural number n.


Sol : Given number = 6n = ( 2 X 3 )n


The prime factors here are 2 and 3 only.


To be end with 0; 6n should have a prime factor 5 and also 2. So,


6n can’t end with zero.


 Class 10 Real Numbers exercise 1.2

SSC Real Numbers


4Q. Explain why 7 X 11 X 13 + 13 and 7 X 6 X 5 X 4 X 3 X 2 X 1 + 5 are composite numbers.


Sol : Given numbers are


7 X 11 X 13 + 13 and


7 X 6 X 5 X 4 X 3 X 2 X 1 + 5


13 ( 7 X 11 + 1 ) and 5 ( 7 X 6 X 4 X 3 X 2 X 1 + 1 )


13 K and 5 L, where K = 78 and


L = 7 X 6 X 4 X 3 X 2 X 1 + 1 = 1009


As the given numbers can be written as product of two numbers, they are composite.



Class 10 Real Numbers exercise 1.2

5Q. How will you show that ( 17 X 11 X 2 ) + ( 17 X 11 X 5 ) is a composite number? Explain.


Sol : ( 17 X 11 X 2 ) + ( 17 X 11 X 5 )


= ( 17 X 11 ) ( 2 + 5 )


= ( 17 X 11 ) ( 7 ) = 187 X 7


Now the given expression is written as a product of two integers and hence it is a composite number.


πŸ‘‰ CLICK HERE FOR REAL NUMBER EXERCISE 1.1 

πŸ‘‰ CLICK HERE FOR REAL NUMBER EXERCISE 1.3

πŸ‘‰ CLICK HERE FOR REAL NUMBER EXERCISE 1.4


Class 10 Real Numbers Exercise 1.2

For Real Number chapter of SSC Examination


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