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**NCERT solutions for Maths Playing with numbers Download as PDF**

## NCERT Solutions for Class 6 Maths Playing with numbers

**Class –VI **

**Mathematics **

**(Ex. 3.5)**

**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 them must be prime.

(f)All numbers which are divisible by 4 must also by divisible by 8.

(g)All numbers which are divisible by 8 must also by divisible by 4.

(h)If a number is exactly divides two numbers separately, it must exactly divide their sum.

(i)If a number is exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

**Answer:** Statements (b), (c), (d), (g) and (h) are true.

**Question** 2.Here are two different factor trees for 60. Write the missing numbe

(a)

(b)

**Answer:** Sol.

(a)

(b)

NCERT Solutions for Class 6 Maths 3.5

**Question** 3.Which factors are not included in the prime factorization of a composite number?

**Answer: **1

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

**Answer: **The greatest four digit number is 9999.

The prime factors of 9999 are 3 x 3 x 11 x 101.

NCERT Solutions for Class 6 Maths 3.5

**Question** 5.Write the smallest 5-digit number and express it in terms of its prime facto

**Answer: **The smallest five digit number is 10000.

The prime factors of 10000 are 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5.

**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 numbe

**Answer: **Sol.

Prime factors of 1729 are 7 x 13 x 19.

The difference of two consecutive prime factors is 6.

NCERT Solutions for Class 6 Maths 3.5

**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:(i) 2 x 3 x 4 = 24

(ii) 4 x 5 x 6 = 120

**Question** 8.The sum of three consecutive numbers is always divisible by 4. Verify this statement with the help of some examples.

**Answer:** 3 + 5 = 8 and 8 is divisible by 4.

5 + 7 = 12 and 12 is divisible by 4.

7 + 9 = 16 and 16 is divisible by 4.

9 + 11 = 20 and 20 is divisible by 4.

NCERT Solutions for Class 6 Maths 3.5

**Question** 9.In which of the following expressions, prime factorization has been done:

(a)24 = 2 x 3 x 4

(b)56 = 7 x 2 x 2 x 2

(c)70 = 2 x 5 x 7

(d)54 = 2 x 3 x 9

**Answer: **In expressions (b) and (c), prime factorization has been done.

**Question** 10.Determine if 25110 is divisible by 45.

[Hint: 5 and 9 are co-prime numbe Test the divisibility of the number by 5 and 9.]**Answer: **The prime factorization of 45 = 5 x 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 x 9 = 45

NCERT Solutions for Class 6 Maths 3.5

**Question** 11. 18 is divisible by both 2 and 3. It is also divisible by 2 x 3 = 6. Similarly, a number is divisible by 4 and 6. Can we say that the number must be divisible by 4 x 6 = 24? If not, give an example to justify your answer.

**Answer: **No. Number 12 is divisible by both 6 and 4 but 12 is not divisible by 24.

**Question** 12.I am the smallest number, having four different prime facto Can you find me?

**Answer:** 2 x 3 x 5 x 7 = 210

## NCERT Solutions for Class 6 Maths 3.5

NCERT Solutions Class 6 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 6 Maths includes text book solutions from Class 6 Maths Book . NCERT Solutions for CBSE Class 6 Maths have total 14 chapters. 6 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 6 solutions PDF and Maths ncert class 6 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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