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3. Playing with Numbers-Exercise 3.5 Mathematics Class 6 In English
Last Updated : 06 March 2026
Get updated solved mathematics for class 6 chapter 3. Playing with Numbers Topic Exercise 3.5 with clear explanations free study material in English medium.
3. Playing with Numbers-Exercise 3.5 Mathematics Class 6 In English
Last Updated : 06 March 2026
3. Playing with Numbers-Exercise 3.5 Mathematics Class 6 In English
3. Playing with Numbers
Exercise 3.5
Exercise 3.5
1. Which of the following statements are true?
(a) If a number is divisible by 3, it must be divisible by 9.
Answer : False
(b) If a number is divisible by 9, it must be divisible by 3.
Answer : True
(c) A number is divisible by 18, if it is divisible by both 3 and 6.
Answer : False
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
Answer : True
(e) If two numbers are co-primes, at least one of them must be prime.
Answer : False
(f) All numbers which are divisible by 4 must also be divisible by 8.
Answer : False
(g) All numbers which are divisible by 8 must also be divisible by 4.
Answer : True
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
Answer : True
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
Answer : False
2. Here are two different factor trees for 60. Write the missing numbers.
Solution:
There are two different way as follow:
3. Which factors are not included in the prime factorization of a composite number?
Solution: 1 and the composite number itself not included in the prime factorization of a composite number.
4. Write the greatest 4-digit number and express it in terms of its prime factors.
Solution: The greatest 4-digit number -
5. Write the smallest 5-digit number and express it in the form of its prime factors.
Solution:
The smallest five diigit number is 10000.
It's tree factor is :
Hence the prime factorisation =
2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
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.
Solution:
Prime factors of 1729 are 7 × 13 × 19.
7. The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.
Solution: 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 × 3 × 4 = 24
(ii) 4 × 5 × 6 = 120
8. The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.
Solution: 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.
9. In which of the following expressions, prime factorisation has been done?
Solution: In expressions (b) and (c), prime factorization has been done.
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].
Solution: The prime factorization 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
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.
Solution: No. Number 12 is divisible by both 6 and 4 but 12 is not divisible by 24.
12. I am the smallest number, having four different prime factors. Can you find me?
Solution: The smallest four prime numbers are 2, 3, 5 and 7.
Hence, the required number is 2 × 3 × 5 × 7 = 210
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NCERT Solutions for Class 6 mathematics Chapter 3. Playing with Numbers Topic Exercise 3.5
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3. Playing with Numbers-Exercise 3.5 Mathematics Class 6 In English
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3. Playing with Numbers-Exercise 3.5 Mathematics Class 6 In English Study Materials For Class 6 to 12
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