- Flashback of IX real Number's
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- Euclid's Division Lemma
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- Proof of Euclid's Division Lemma
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- HCF (Highest common factor)
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- What is Prime Numbers
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- What is Composite Numbers
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- Fundamental Theorom of Arithmetic
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- HCF and LCM by prime factorization method
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- Irrational Numbers
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- How to prove the irrational numbers or Rational numbers

- Real number problem and Solutions
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- Real number Worksheet
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- Real number problems
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- Real number Important questions

Given below are the

a) Concepts questions

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

1) Use Euclid’s algorithm to find the HCF of 4052 and 12576.

2) show that any positive odd integer is of the form 4q + 1 or 4q + 3, where is some integer.

3) Find HCF and LCM of following using Fundamental Theorem of Arithmetic method.

448, 1008 and 168

4) Find the HCF and LCM of following using Fundamental Theorem of Arithmetic method 377, 435 and 667.

5) Find HCF of numbers 134791, 6341 and 6339 by Euclid’s division algorithm.

6) Find the least positive integer which when diminished by 5 is exactly divisible by 36 and 54.

7) Find HCF and LCM of 12, 63 and 99 using prime factorisation method.

8) If the HCF of 144 and 180 is expressed in the form 13m – 3, find the value of m.

9) Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they start ringing together, after how much time will they next ring together?

10) In sports Day activities of a school, three cyclists start together and can cycle 48 km, 60 km and 72 km a day round the field. The field is circular, whose circumference is 360 km. After how many rounds they will meet again?

11) LCM of two numbers is 2295 and HCF is 9. If one of the numbers is 153, find the other number.

12) Express 111972 as a product of its prime factors.

14) The traffic lights at three different road – crossing change after every 36 seconds, 60 seconds and 72 seconds. If they change simultaneously at 8 a. m. after, what time will they change again simultaneously?

15) Using prime factorization method, find HCF and LCM of 80, 124 and 144. Also, show that HCFX LCM = Product of three numbers.

17) Determine the prime factorization of 45470971 positive integers.

18) A rectangular courtyard is 18m 72 cm long and 13m 20cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

19) Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).

20) What is the smallest number that, when divided by 35, 56 and 91 leaves remainders of 7 in each case?

Answer

1) 4

3) 56, 4032

4) 29, 130065

5)1

6) 113

7) 3, 2772

8)m = 3

9) 60 minutes

10) 2 rounds

14) 360 seconds

15) 4, 22320

17) 7

18) 4290

19)2520

20) 3647

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