## MCQ on Prime Time Class 6

### Class 6 Maths Chapter 5 MCQ Prime Time

Choose the right answer:

Question 1.

The number with unit digit 0 or 5 is divisible by:

(a) 2

(b) 3

(c) 4

(d) 5

Answer:

(d) 5

Question 2.

The number with unit digit 8 is divisible by:

(a) 2

(b) 3

(c) 4

(d) 5

Answer:

(a) 2

Question 3.

The number with unit digit by:

(a) 5

(b) 10

(c) 15

(d) 2

Answer:

(b) 10

Question 4.

1170 is not divisible by:

(a) 10

(b) 9

(c) 5

(d) 4

Answer:

(d) 4

Question 5.

Prime factorization of 54 is:

(a) 2 × 27

(b) 2 × 3 × 9

(c) 54 × 1

(d) 2 × 3

Solution:

(d)

Question 6.

2 × 3 × 7 is the prime factorization of

(a) 21

(b) 1237

(c) 237

(d) 42

Solution:

(d)

Question 7.

Fill in the blanks:

(i) ___________ is neither a prime nor a composite number.

Answer: 1

(ii) 2. ___________ is the smallest prime number.

Answer: 2

(iii) 3. ___________ is the only even prime number.

Answer: 2

(iv) 1 is neither ___________ nor ___________.

Answer: Prime, composite

(v) The number which has more than 2 factors is called a ___________ number.

Answer: Composite

(vi) ___________ is the smallest composite number.

Answer: 4

(vii) A prime number has only ___________ factors.

Answer: 2

(viii) The smallest odd prime number is ___________.

Answer: 3

(ix) Number foimed by multiplying the first three prime numbers is ___________.

Answer: 30

(x) Fill in the smallest digit to make the number divisible by 5 : 7164_____, 32197_______

Answer: 0,0

(xi) The smallest digit to make the number divisible by: 3 : 1____43, 47____05, ____316

Answer: 1, 2, 2

(xii) The smallest digit to make the number divisible by: 6 : ____428, 9____52, 721____

Answer: 1, 2, 2

(xiii) The smallest digit to make the number divisible by: 4 : 2462____, 91________, 670____

Answer: 0, 00, 0

(xiv) The smallest digit to make the number divisible by: 8 : 1232_____, 59 16, 4642_

Answer: 0, 0, 4

Question 8.

State true (T) or false (F):

(i) 1 is a prime number.

Answer: False

(ii) There are 8 prime numbers between 1-20.

Answer: True

(iii) 12 is a prime number.

Answer: False

(iv) 21 has 4 factors – 1, 3, 7 and 21.

Answer: True

(v) 4, 6, 7, 8 and 9 are composite numbers,

Answer: False (7 is a prime number)

(vi) Consecutive numbers are always coprime, (whose HCF is 1)

Answer: True

(vii) The sum of primes cannot be a prime.

Answer: False

2 + 3 = 5 is a prime number.

(viii) The product of primes cannot be a prime.

Answer: True

The product of primes is a composite number.

(ix) An even number is composite.

Answer: False

Even number 2 is not composite.

(x) Two consecutive numbers cannot be both primes.

Answer: False

The numbers 2 and 3 are consecutive and prime numbers.

(xi) Odd numbers cannot be composite.

Answer: False

9 is an odd number and is composite having factors 1, 3 and 9.

(xii) Odd numbers cannot be written as sum of primes.

Answer: False

9 is an odd number and the sum of prime number 7 + 2 = 9.

(xiii) A number and its successor are always co-primes.

Answer: True

A number and its successor have only one common factor.

(xiv) 5 × 33 is the prime factorization of 165.

Answer: False

(xv) If two numbers are divisible by a number, then their sum, difference and product are also divisible by that number.

Answer: True

(xvi) The largest 4-digit number divisible by 11 is 9999.

Answer: True

(xvii) Numbers not divisible by 2 are called even numbers.

Answer: False

Question 9.

Match the following:

Match the Columns:

Column A | Column B |

(i) 2023 | (a) divisible by 3 |

(ii) 24804 | (b) divisible by 11 |

(iii) 12892 | (c) divisible by 8 |

(iv) 6016 | (d) divisible by 7 |

Answer:

Column A | Column B |

(i) 2023 | (d) divisible by 7 |

(ii) 24804 | (a) divisible by 3 |

(iii) 12892 | (b) divisible by 11 |

(iv) 6016 | (c) divisible by 8 |

Question 10.

What is the difference between Factors and Multiples?

Solution:

The major differences between factors and multiples are provided below:

Factors | Multiples |

A factor of a number is defined as an exact divisor of the given number. | A multiple of a number is defined as a number that is obtained by multiplying it by a natural number. |

For example, the factors of 20 are 1, 2, 4, 5, 10, and 20. | For example, the multiples of 20 are 20, 40, 60, 80, 100, etc. |

Question 11.

Write the first 5 multiples of each of the following:

(a) 23

(b) 40

Solution:

(a) The first five multiples of 23 are 23,46, 69, 92, 115.

(b) The first five multiples of 40 are 40, 80, 120, 160, 200.

Question 12.

Write down the factors and multiples of 25.

Solution:

The factors of 25 are 1, 5 and 25

The multiples of 25 are 25, 50, 75, 100, 125, 150, and so on.

Question 13.

Are the multiples of 4 even?

Solution:

Multiples of 4 are: 4, 8, 12, 16, 20 ,

Yes, the multiples of 4 are even. Since 4 is an even number, the multiples of 4 are also even.

Question 14.

Are the multiples of 3 always the multiples of 6?

Solution:

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21,… . Hence, the multiples of 3 are not always the multiples of 6.

As 9, 15, 21 are not multiples of 6.

Question 15.

Find the common factors of:

(a) 4, 8 and 12

(b) 5,15 and 25

Solution:

(a) Given numbers are: 4, 8 and 12

Factors of 4 are 1,2, 4

Factors of 8 are 1, 2, 4, 8

Factors of 12 are 1, 2, 3, 4, 6, 12

Therefore, the common factors of 4, 8 and 12 are 1,2, and 4.

(b) Given numbers are: 5, 15 and 25

Factors of 5 are 1, 5

Factors of 15 are 1, 3, 5, 15

Factors of 25 are 1, 5, 25

Therefore, the common factors of 5, 15, and 25 are 1 and 5.

Question 16.

What is the greatest common factor of 3 and 15?

Solution:

The factors of 3 are 1 and 3.

The factors of 15 are 1, 3, 5 and 15.

Therefore, the greatest common factor of 3 and 15 is 3.

Question 17.

Find the greatest common factor of 10 and 6.

Solution:

The factors of 6 are 1, 2, 3 and 6.

The factors of 20 are 1,2, 4, 5, 10 and 20.

Thus, the greatest common factor of 6 and 20 is 2.

Question 18.

Find the common multiples of 3 and 5.

Solution:

The multiples of 3 are 3, 6, 9, 12, 15, 18,21,v 24, 27, 30,..

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35,40,…

Therefore, the common multiples of 3 and 5 are 15, 30, 45, 60, and so on.

Question 19.

Is 6 a prime number or composite number?

Solution:

6 is a composite number as it can be divided by more than 2 numbers 1,2,3 and 6.

2. 1 is not considered as a prime number, why? Solution:Because it does not have distinct two factors

(i.e., 1 and the number itself are the same)

Question 20.

Which of the following is a prime number?

(a) 23

(b)18

(c) 25

(d) 15

Solution:

(a) 23 = 1 × 23

Hence, 23 is a prime number.

(b) Since 18 = 1 × 18 or 6 × 3

Hence, 18 is not a prime number.

(c) Since 25 = 1 × 25 or 5× 5

Hence, 25 is not a prime number.

(d) Since 15 = 1 × 15 or 3 × 5

Hence, 15 is not a prime number.

Hence, the option (a) is correct.

Question 21.

The numbers 13 and 31 are prime numbers. Both these numbers have the same digits 1 and 3. Find such pairs of prime numbers up to 100.

Solution:

17 and 71, 37 and 73, 79 and 97 are the required pairs of prime numbers up to 100.

Question 22.

List all the composite numbers between the following:

(i) 10 and 18

(ii) 61 and 69

(iii) 91 and 96

Answer:

(i) Composite numbers between 10 and 18 are 12, 14, 15 and 16.

(ii) Composite numbers between 61 and 69 are 62, 63, 64, 65, 66 and 68.

(iii) Composite numbers between 91 and 96 are 92, 93, 94 and 95.

Question 23.

Choose all prime numbers:

12 19 7 8 9 11 15

13 24 27 23 34 37 36

Answer:

19,7,11,13,23,37

Question 24.

Write all the composite numbers less than 30.

Answer:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28

Question 25.

Write all the prime numbers less than 20.

Answer:

2,3,5,7,11,13,17,19

Question 25.

Write all the composite numbers between 1 and 40.

Answer:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40.

Question 26.

Check whether or not the following are composite numbers

(i) 98

Answer:

The factors of 98 are 1, 2, 7, 14, 49 and 98.

So, 98 is a composite number.

(ii) 47

Answer:

The factors of 47 are 1 and 47.

So, 47 is not a composite number. It is a prime number.

(iii) 35

Answer:

The factors of 35 are 1, 5, 7, 35.

So, 35 is a composite number.

(iv) 69

Answer:

The factors of 69 are 1, 3, 23, 69.

So, 69 is a composite number.

(v) 108

Answer:

The factors of 108 are 1,2, 3,4, 6, 9, 12, 18, 27,36, 54, and 108.

So, 108 is a composite number.

(vi) 19

Answer:

The factors of 19 are 1 and 19 So, 19 is not .a composite number.

(vii) 21

Answer:

The factors of 21 are 1, 3, 7, 21.

So, 21 is a composite number.

(viii) 103

Answer:

The factors of 103 are 1 and 103

So, 103 is not a composite number.

Question 19.

Check if the given pair of numbers are co-primes:

(i) 15 and 38

Answer:

Here factors of 15 are 1, 3, 5, 15 and factors of 38 are 1,2, 19, 38

∴ HCF of 15 and 38

= common factors of 15 and 38 = 1

Since HCF of 15 and 38 is 1.

Hence 15 and 38 are co-primes.

(ii) 25 and 26

Answer:

Here factors of 25 are 1, 5, 25 and factors of 26 are 1,2, 13, 26

∴ common factors of 25 and 26 = 1

Since HCF of 25 and 26 is 1.

Hence 25 and 26 are co-primes.

(iii) 12 and 18

Answer:

Here factors of 12 are: 1, 2, 3, 4, 6, 12 and factors of 18 are: 1, 2, 3, 6, 9, 18

∴ HCF of 12 and 18

= common factors of 12 and 18 = 1,2 and 3

Since 1,2 and 3 are factors of 12 and 18.

Hence they are not co-primes.

Question 27.

Find five pairs of co-prime numbers.

Answer:

(3, 5); (4, 9); (7, 10); (20, 29); (31, 65).

Question 28.

Are 40 and 78 co-prime?

Answer:

Since two even numbers always have two

common factors, 1 and 2, they can never be

co-prime numbers. Thus, 40 and 78 are not co-prime numbers.

Question 29.

Find the prime factorization of 126000.

Answer:

Here,

Hence, the prime factorization of 126000

2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5 × 7

Question 30.

List the common prime factors of 256 and 156.

Answer:

Prime factorization of

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Prime factorization of 156 = 2 × 2 × 3 × 3

The common prime factor of 256 and 156 is 2.

Question 31.

List the common factors of 152 and 76.

Answer:

Prime factorization of 152 = 2 × 2 × 2 × 19

Prime factorization of 76 = 2 × 2 × 19

The common prime factors of 152 and 76 are 2 and 19.

Question 32.

Find the prime factorization of the following numbers:

(i) 18

Answer:

18 = 1 × 2 × 3 × 3

(ii) 39

Answer:

39 = 1 × 3 × 13

(iii) 385

Answer:

385 = 1 × 5 × 7 × 11

(iv) 45

Answer:

45 = 1 × 3 × 3 × 5

(v) 52

Answer:

52 = 1 × 2 × 2 × 13

(vi) 64

Answer:

64 = 2 × 2 × 2 × 2 × 2 × 2

(vii) 390

Answer:

390 = 2 × 3 × 5 × 13

(viii) 2520

Answer:

2520 = 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7

(ix) 1210

Answer:

1210 = 2 × 5 × 11 × 11

(x) 1260

Answer:

1260 = 1 × 2 × 2 × 3 × 3 × 5 × 7

(xi) 1024

Answer:

1024 = 1 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

(xii) 2520

Answer:

2520 = 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7

Question 33.

Write down the divisibility rule for 9.

Answer:

The sum of the digits of the given number should be divisible by 9.

For example, 2979 is divisible by 9. (i.e.,) 2+9+7+9 = 27, which is divisible by 9.

Question 34.

Which of the following numbers are divisible by 2, 5 and 10?

(i) 149

(ii) 19400

(iii) 720345

(iv) 125370

(v) 3000000

Answer:

(ii) 19400

(iv) 125370

(v) 3000000

Question 35.

Check whether the numbers are divisibility by 4:

(i) 23408

(ii) 100246

Answer:

(i) Given number is 23408

Here last 2 digits of 23408 is 08.

it is divisible by 4. (∵ \(\frac{8}{2}\) = 2)

Hence 23408 is divisible by 4.

(ii) Given number is 100246

Now last 2 digits of 100246 is 46 which is not divisible by 4.

Hence 100246 is not divisible by 4.

Question 36.

In each of the following numbers without doing actual division, determine Whether the first number is divisible by the second number:

(i) 3409122;6

(ii) 11309634; 8

(iii) 3501804; 4

Answer:

(i) Let’s determine if 3409122 is divisible by 6.

The divisibility rule for 6 combines the rules for 2 and 3.

Here 3409122 is even number because its last digit is 2.

Hence given number is divisible by 2.

Also the sum of its digits is

3 + 4 + 0 + 9 + 1 + 2 + 2 = 21

which is divisible by 3.

Thus given number is also divisible by 3.

Hence 3409122 is also divisible by 6.

(ii) Given number is 11309634

Here last 3 digits of 11309634 is 634

Now

which is not divisible by 8.

Hence 11309634 is not divisible by 8.

(iii) Given number is 3501804

and last 2 digits of 3501804 is 04.

It is divisible by 4.

Hence 3501804 is divisible by 4.

Question 37.

Which of the two nearest numbers to 19506 are divisible by 9?

Answer:

19503, 19512