Real Numbers

Topics in this chapter

• Euclid’s Division Lemma
• Prime Factorisation Theorem
• HCF, LCM, and Divisibility
• Rational Number Decimal Expansions
• Irrationality and Real Number Proofs

Cheat sheet

Practice questions

1. Question 1Q-965656

   What is the HCF of the smallest prime number and the smallest composite number?

   1. A.1
   2. B.2
   3. C.4
   4. D.8
   See the answer and solution
2. Question 2Q-8C7F18

   Let $a$ and $b$ be two positive integers such that $a = x^3 y^2$ and $b = x y^3$, where $x$ and $y$ are prime numbers. What is $\text{HCF}(a, b)$?

   1. A.$x^3 y^3$
   2. B.$x y$
   3. C.$x y^2$
   4. D.$x^2 y^2$
   See the answer and solution
3. Question 3Q-05A6AB

   The decimal expansion of the rational number $\frac{43}{2^4 \times 5^3}$ will terminate after how many places of decimals?

   1. A.3
   2. B.4
   3. C.5
   4. D.7
   See the answer and solution
4. Question 4Q-D3340C

   If two positive integers $p$ and $q$ can be expressed as $p = ab^2$ and $q = a^3b$, where $a, b$ are prime numbers, then what is the LCM($p, q$)?

   1. A.$ab$
   2. B.$a^2b^2$
   3. C.$a^3b^2$
   4. D.$a^3b^3$
   See the answer and solution
5. Question 5Q-2B577F

   Given that $\text{HCF}(306, 657) = 9$, find $\text{LCM}(306, 657)$.

   1. A.22338
   2. B.22138
   3. C.22392
   4. D.22528
   See the answer and solution