Students can practice TS 6th Class Maths Solutions Chapter 3 Playing with Numbers InText Questions to get the best methods of solving problems.

## TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise InText Questions

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Question 1.

Are 953, 9534, 900, 452 divisible by 2? Also check by actual division.

Answer:

(i) The given number is 953.

This number is divisible by 2 because it has not any one of the digits 0, 2, 4, 6 or 8 in its units place.

(ii) The given number is 9534.

This number is divisible by 2 because it has 4 in its units place.

(iii) The given number is 900.

This number is divisible by 2 because it has ‘0’ in its units place.

(iv) The given number is 452.

This number is divisible by 2 because it has 2 in its units place.

Do This

Check whether the following numbers are divisible by 3 ?

(i) 45986

Answer:

The given number is 45986.

Sum of the digits = 4 + 5 + 9 + 8 + 6 = 32

32 is not a multiple of 3.

So the given number is not divisible by 3.

(ii) 36129

Answer:

The given number is 36129.

Sum of the digits = 3 + 6 + 1 + 2 + 9 = 21

21 is a multiple of 3.

So the given number is divisible by 3.

(iii) 7874

Answer:

The given number is 7874.

Sum of the digits = 7 + 8 + 7 + 4 = 26

26 is not a multiple of 3.

So the given number is not divisible by 3.

Try These

Question 1.

Is 7224 divisible by 6 ? Why ?

Answer:

The given number has 4 in its units place.

So it is divisible by 2.

The sum of the digits of the given number is 7 + 2 + 2 + 4 = 15.

It is a multiple of 3.

So the given number is divisible by 3.

If a number is divisible by both 2 and 3 then it is divisible by 6 also.

Question 2.

Give two examples of 4 digit numbers which are divisible by 6.

Answer:

9648 and 3756.

Question 3.

Can you give an example of a number which is divisible by 6 but not by 2 and 3, why ?

Answer:

A number is divisible by 6 only when it is divisible by 2 and 3.

So, it is not possible to give an example for such number.

Do This

Question 1.

Test whether 9846 is divisible by 9 ?

Answer:

Number = 9846

Sum of the digits = 9 + 8 + 4 + 6 = 27 27

\(\frac{27}{9}\) = 3 9

∴ 9846 is divisible 9.

Question 2.

Without acutal division, find whether 8998794 is divisible by 9 ?

Answer:

Number = 8998794

Sum of the digits = 8 + 9 + 9 + 8 + 7 + 9 + 4 = 54

\(\frac{54}{9}\) = 6

∴ 8998794 is divisible by 9.

Question 3.

Check whether 786 is divisible by both 3 and 9 ?

Answer:

Number = 786

Sum of the digits = 7 + 8 + 6 = 21

\(\frac{21}{3}\) = 7

So 786 is divisible by 9.

But 21 is not divisible by 9.

So 786 is not divisible by 9.

Do This

Question 1.

Find the factors of 80.

Answer:

Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.

Question 2.

Do all the factors of a given number divide the number exactly ? Find the factors of 28 and verify by division.

Answer:

Yes, all the factors of a given number divide the number exactly.

Factors of 28 are 1, 2, 4, 7, 14, 28.

Verification:

\(\frac{28}{28}\) = 1, \(\frac{28}{14}\) = 2, \(\frac{28}{7}\) = 4, \(\frac{28}{4}\) = 7, \(\frac{28}{2}\) = 14

Question 3.

3 is a factor of 15 and 24. Is 3 a factor of their difference also ?

Answer:

Yes. (The difference between 15 and 24 is 9 and 9 is a multiple of 3.)

Try These

Question 1.

What is the smallest prime number?

Answer:

The smallest prime number is 2.

Question 2.

What is the smallest composite number?

Answer:

The smallest composite number is 4.

Question 3.

What is the smallest odd composite number?

Sol.

The smallest odd composite number is 6.

Question 4.

Give 5 odd and 5 even composite numbers.

Answer:

The odd composite numbers are

9, 15, 21, 25, 27 etc.

The even composite numbers are

4, 6, 8, 10, 12 etc.

Question 5.

Is 1 prime or composite and why?

Answer:

The number 1 has only one factor i.e. (itself). So, 1 is neither prime nor composite.

Question 6.

Can you guess a prime number which when on reversing Its digits, gives another prime number?

(Hint : Take a 2 digit prime number)

Answer:

13 is a prime number. On reversing its digits it becomes 31, which is also a prime number.

Question 7.

You know 311 is a prime number. Can you find the other two prime numbers just by rearranging the digits?

Answer:

Given prime number is 311.

The other two prime numbers just by rearranging the digits are 113 and 131.

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From the following numbers identify different pairs of co-primes. 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Answer:

(2, 3); (2, 5); (2, 7); (3, 5); (3, 7); (5, 7)

Do This

Question 1.

Write the prime factors of 28 and 36 through division method.

Answer:

∴ Prime factors of 36 is 2 × 2 × 3 × 3

Question 2.

Write the prime factors of 42 by factor tree method.

Answer:

∴ Prime factors of 42 is 2 × 3 × 7

Do This

Find the HCF of 12, 16 and 28 by prime factorization method.

Answer:

The common factors of 12, 16 and 28 is 2 × 2 = 4

Hence, HCF of 12, 16 and 28 is 4.

Do This

Find the HCF of 28, 35 and 49 by division method^

Answer:

First find the HCF of any two numbers.

Let us find the HCF of 28 and 35

Last divisor is 7

∴ HCF of 28 and 35 is 7.

Then find the HCF of the third numbern and the HCF of first two numbers.

Let us find the HCF of 49 and 7.

HCF of 49 and 7 is 7.

∴ The HCF of 28, 35 and 49 is 7.

Think, Discuss and Write

What is the HCF of any two

(i) Consecutive numbers ?

Answer:

The HCF of any two consecutive numbers is 1.

(ii) Consecutive even numbers ?

Answer:

2

(iii) Consecutive odd numbers ?

Answer:

1 (one)

What do you observe ? Discuss with your friends.

Answer:

It was observed that the HCF of two consecutive numbers and consecutive odd numbers is same, i.e., 1.

Try This

Question 1.

find the LCM of

(i) 3, 4

(ii) 10, 11

(iii) 5, 6, 7

(iv) 10, 30

(v) 4, 12, 24

(vi) 3, 12

What do you observe ?

Answer:

(i) LCM of 3 and 4 = 3 × 4 = 12

(ii) LCM of 10 and 11 = 10 × 11 = 110

(iii) LCM of 5, 6 and 7 = 5 × 6 × 7 = 210

(iv) LCM of 10 and 30 = 10 × 1 × 3 = 30

(v) LCM of 4, 12 and 24 = 4 × 3 × 2 = 24

(vi) LCM of 3 and 12 = 3 × 4 = 12

It is observed that the LCM of two numbers will be their product, if the given numbers have no common factor except 1.

Think, Discuss and Write

When will the LCM of two or more numbers be their own product ?

Answer:

If the numbers are co-primes or relatively prime numbers then the LCM of two or more numbers be their own product.

Think, Discuss and Write

Question 1.

What is the LCM and HCF of twin prime numbers?

Answer:

Let the twin primes may be (3, 5)

LCM of 3, 5 is their product 3 × 5 = 15

HCF of 3, 5 is 1.

(for any type of twin prime)

Question 2.

Interpret relationship between LCM and HCF of any two numbers?

Answer:

Consider the two numbers be 14 and 21.

Now find LCM of 14 and 21.

∴ LCM of 14 and 21 = 7 × 2 × 3 = 42

Now find HCF of 14 and 21.

∴ HCF of 14 and 21 is 7.

Relation between LCM and HCF of 14 and 21:

42 × 7 = 14 × 21 = 294

Product of LCM and HCF of two numbers = Product of two numbers.

Do This

Divisibility Rule for 4:

Question 1.

Is 100000 is divisible by 4? Why?

Answer:

100000 = 1000 × 100

The given number is a multiple of 100.

We know, 100 is divisible by 4.

∴ The given number (i.e., 100000) is divisible by 4.

Question 2.

Give an example of a 2 digit number that is divisible by 2 but not divisible by 4?

Answer:

22, 26, 30, 34, 38 98 .

All the above two digit numbers are divisible by 2 but not divisible by 4.

Do This

Question 1.

Is 76104 divisIble by 8?

Answer:

The number formed by the last three digits is 104. It is divisible by 8.

Hence, the given number is divisible by 8.

Question 2.

Write the numbers that are divisible by 8 and lie between 100 and 200.

Answer:

104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192 are ail divisible by 8.

They lie between 100 and 200.

Page No. 92 (45)

Divisibility Rule for 11:

Using the division rule of ’11’. Fill the following table.

Answer:

1221 is a Palindrome number, which on reversing their digits gives the same number.

Thus, every Palindrome number with even number of digits, is always divisible by 11.

Write a Palindrome number of 6 digits and verify whether it is divisible by 11 or not.

Answer:

Palindrome number which on reversing their digits gives the same number.

Every Palindrome number with even number is always divisible by 11.

∴ The 6 digited Palindrome number is 123321. It is divisible by 11.