NCERT Class 6 Math Exercise 3.5 Solution of Chapter 3 Playing with Numbers with explanation. Here we provide Class 6 Maths all Chapters in Hindi for cbse, HBSE, Mp Board, UP Board and some other boards.

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NCERT Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.5 Solution in english Medium.

**Class 6 Maths Chapter 3 Exercise 3.5 Solution**

**Question 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. If a number is divisible by 18, it must be 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 thme must be prime.**

**F. All numbers which are divisible by 4 must 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 divides the two numbers separately.**

**Answer.**

statements B, C, D, G, and H aer true.

Question 2.

Here are two different factor trees for 60. Write the missing numbers.

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**Question 3.**

**Which factors are not included in the prime factorisation of a composite number?**

**Answer.**

1 and the number itself are the factor which is not included in the prime factorisation of a composite number.

**Question 4.**

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

**Answer.**

The greatest 4 digit number = 9999

The prime factors of 9999 are 3x3x11x101.

**Question 5.**

**write the smallest 5 digit number and express it in terms of its prime factors.**

**Answer**.

The smallest five digit number is 10000.

The prime factors of 10000 are 2x2x2x2x5x5x5x5.

**Question 6.**

**Find all the prime factors of 1729 and arrange them in ascending order.**

**Now state the relation, if any between , two consecutive prime numbers.**

**Answer.**

Prime factors of 1729 are 7x13x19.

The difference of two consecutive prime factors is 6.

**Question 7.**

**The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.**

**Answer.**

Among the three consecutive numbers, there must be one even number and one multiple of 3. Thus, the product must be multiple of 6.

Example: 2x3x4 = 24.

4x5x6 = 120.

**Question 8.**

**The sum of two consecutive odd numbers is always divisible by 4. Verify this statement with the help of some examples.**

**Answer.**

3 + 5 = 8, is divisible by 4.

5 + 7 = 12, is divisible by 4.

7 + 9 = 16, is divisible by 4.

**Question 9.**

**In which of the following expressions, prime factorisation has been done:**

**A. 24 = 2x3x4**

**B. 56 = 7x2x2x2**

**C. 70 = 2x5x7**

**D. 54 = 2x3x9**

**Answer.**

In expressions B and C, prime factorisation has been done.

**Question 10.**

**Determine if 25110 is divisible by 45.**

**Answer.**

The prime factorisation of 45 = 5×9

25110 is divisible by 5 as 0 is at its unit place.

25110 is divisible by 9 as sum of digits is divisible by 9.

therefore, the number must be divisible by 5×9 = 45.

**Question 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.**

**Answer.**

No.

Number 12 is divisible by both 6 and 4 but is 12 is not divisible by 24.

**Question 12.**

**I am the smallest number, having four different prime factors. Can you find me?**

**Answer.**

The smallest four prime numbers are 2, 3, 5 and 7.

Hence, the required number is 2x3x5x7 = 210.