Mathematics Class 6 NCERT Solutions: Chapter 3 Playing With Numbers Exercise 3.5-Part 1

Download PDF of This Page (Size: 362K)

Prime vs. composite numbers

Prime vs. Composite Numbers

Prime vs. composite numbers

Q.1 Which of the following statements are true:

(a) If a number is divisible by 3, it must be divisible by .

Answer: False

Ex. 6 is divisible by 3, but not by 9.

(b) If a number is divisible by 9, it must be divisible by .

Answer: True

So, if a number is divisible by 9, it must be divisible by .

(c) If a number is divisible by 18, it must be divisible by both .

Answer: False

Ex. 30 is divisible by 3 and 6 both, but it is not divisible by 18.

(d) If a number is divisible by 9 and 10 both, then it must be divisible by .

Answer: True

So, If a number is divisible by 9 and 10 both, then it will also be divisible by 90.

(e) If two numbers are co-primes, at least one of them must be prime.

Answer: False

Ex. 15 and 32 are co-prime and also composite.

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

Answer: False

Ex. 20 is divisible by 4 but not by 8.

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

Answer: True

Ex.

So, if a number is divisible by 8, then it will also be divisible by 2 and 4.

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

Answer: True

Ex. 2 divide 4 and 8 as well as 12.

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

Answer: False

Ex. 2 divides 14, but does not divide 9 and 5.

Q.2 Here are two different factor trees for 60. Write the missing numbers.

(a)

Image of Two Different Factor Trees For 60 Without Answer - 1

Image of Two Different Factor Trees for 60 Without Answer - 1

Image of Two Different Factor Trees For 60 Without Answer - 1

Answer:

As and

Image of Two Different Factor Trees For 60 With Answer - 1

Image of Two Different Factor Trees for 60 with Answer - 1

Image of Two Different Factor Trees For 60 With Answer - 1

(b)

Image of Two Different Factor Trees For 60 Without Answer - 2

Image of Two Different Factor Trees for 60 Without Answer - 2

Image of Two Different Factor Trees For 60 Without Answer - 2

Answer:

As ,

Image of Two Different Factor Trees For 60 With Answer - 2

Image of Two Different Factor Trees for 60 with Answer - 2

Image of Two Different Factor Trees For 60 With Answer - 2

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

Answer:

1 is the factor which is not included in the prime factorization of a composite number.

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

Answer: The greatest 4-digit number =

Image of Greatest 4-Digit Number And Express It

Image of Greatest 4-Digit Number and Express It

Image of Greatest 4-Digit Number And Express It

The prime factors of are