NCERT Class 6 Mathematics Third Chapter Playing with Numbers Exercise 3.5 Solutions
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. = F
(b) If a number is divisible by 9, it must be divisible by 3. = T
(c) A number is divisible by 18, if it is divisible by both 3 and 6. = F
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90. = T
(e) If two numbers are co-primes, at least one of them must be prime. = F
(f) All numbers which are divisible by 4 must also be divisible by 8. = F
(g) All numbers which are divisible by 8 must also be divisible by 4. = T
(h) If a number exactly divides two numbers separately, it must exactly divide their sum. = T
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately. = F
(2) Here are two different factor trees for 60. Write the missing numbers.
(3) Which factors are not included in the prime factorization of a composite number?
Ans: 1 and the number itself.
(4) Write the greatest 4-digit number and express it in terms of its prime factors.
Ans: 9999 = 3 × 3 × 11 × 101
(5) Write the smallest 5-digit number and express it in the form of its prime factors.
Ans: 10000 = 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: 1729 = 7 × 13 × 19
The difference between two consecutive prime factors is 6.
(7) The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.
Solution: (i) 2 × 3 × 4 = 24 is divisible by 6.
(ii) 5 × 6 × 7 = 210 is divisible by 6.
(8) The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.
Ans: The sum of two consecutive odd numbers is never divisible by 4.
(9) In which of the following expressions, prime factorization has been done?
Ans: (b) 56 = 7 × 2 × 2 × 2
(c) 70 = 2 × 5 × 7
(10) Determine if 25110 is divisible by 45.
Solution: Yes, 25110 = 45 × 558
(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.
Ans: No, Number 12 is divisible by 4 and 6; but 12 is not divisible by 24.
(12) I am the smallest number, having four different prime factors. Can you find me?
Ans: 2 × 3 × 5 × 7 = 210
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