Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

Answer :

The greatest 4-digit number = 9999

$$
\begin{array}{|l}
\llap{3~~~~} 9999 \\ \hline
\llap{3~~~~} 3333 \\ \hline
\llap{11~~~~} 1111 \\ \hline
\llap{101~~~~} 101 \\ \hline
1
\end{array}
$$
Hence, the prime factors of 9999 = 3 x 3 x 11 x 101.

- Q. 1. Which of the following statements are true? (a) If a number is divisible by 3, it must be divisible by 9. (b) If a number is divisible by 9, it must be divisible by 3. (c) A number is divisible by 18, if it is divisible by both 3 and 6. (d) If a number is divisible by 9 and 10 both, then it must be divisible by 90. (e) If two numbers are co-primes, at least one of them must be prime. (f) All numbers which are divisible by 4 must also be divisible by 8. (g) All numbers which are divisible by 8 must also be divisible by 4. (h) If a number exactly divides two numbers separately, it must exactly divide their sum. (i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
- Q.2 Here are two different factor trees for 60. Write the missing numbers.
- Q.3 Which factors are not included in the prime factorisation of a composite number?
- Q. 5. Write the smallest 5-digit number and express it in the form of its prime factors.
- Q.6. Find all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any; between two consecutive prime factors.
- Q.7. The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.
- Q.8. The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.
- Q.9. In which of the following expressions, prime factorisation has been done? (a) 24 = 2 × 3 × 4 (b) 56 = 7 × 2 × 2 × 2 (c) 70 = 2 × 5 × 7 (d) 54 = 2 × 3 × 9
- 10. Determine if 25110 is divisible by 45. [Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9].
- Q.11. 18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by 4 × 6 = 24? If not, give an example to justify your answer.
- Q.12. I am the smallest number, having four different prime factors. Can you find me?

- NCERT solutions for class 6 maths chapter 1 Knowing Our Numbers
- NCERT solutions for class 6 maths chapter 2 Whole Numbers
- NCERT solutions for class 6 maths chapter 3 Playing with Numbers
- NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas
- NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes
- NCERT solutions for class 6 maths chapter 6 Integers
- NCERT solutions for class 6 maths chapter 7 Fractions
- NCERT solutions for class 6 maths chapter 8 Decimals
- NCERT solutions for class 6 maths chapter 9 Data Handling
- NCERT solutions for class 6 maths chapter 10 Mensuration
- NCERT solutions for class 6 maths chapter 11 Algebra
- NCERT solutions for class 6 maths chapter 12 Ratio and Proportion
- NCERT solutions for class 6 maths chapter 13 Symmetry
- NCERT solutions for class 6 maths chapter 14 Practical Geometry

- NCERT solutions for class 6 science chapter 1 Respiratory system, simple machine & elements compounds
- NCERT solutions for class 6 science chapter 1 Food: Where Does It Come From?
- NCERT solutions for class 6 science chapter 2 Components of Food
- NCERT solutions for class 6 science chapter 3 Fibre to Fabric
- NCERT solutions for class 6 science chapter 4 Sorting Materials into Groups
- NCERT solutions for class 6 science chapter 5 Separation of Substances
- NCERT solutions for class 6 science chapter 6 Changes Around us
- NCERT solutions for class 6 science chapter 7 Getting to Know Plants
- NCERT solutions for class 6 science chapter 8 Body Movements
- NCERT solutions for class 6 science chapter 9 The Living Organisms — Characteristics and Habitats
- NCERT solutions for class 6 science chapter 10 Motion and Measurement of Distances
- NCERT solutions for class 6 science chapter 11 Light, Shadows and Reflections
- NCERT solutions for class 6 science chapter 12 Electricity and Circuits
- NCERT solutions for class 6 science chapter 13 Fun with Magnets
- NCERT solutions for class 6 science chapter 14 Water
- NCERT solutions for class 6 science chapter 15 Air Around us