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Answer :

We know that the smallest 4 prime numbers are 2, 3, 5 and 7.

Hence, the required number = 2 x 3 x 5 x 7 = 210

- 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.4 Write the greatest 4-digit number and express it in terms of its prime factors.
- 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.

- 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
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- 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

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