Playing With Numbers — Multiple Choice Questions

A number is divisible by 5 and 8 both, then it must be divisible by:

1. 20

2. 15

3. 40

4. 80

Answer

A number divisible by both 5 and 8 must be divisible by their L.C.M.

Since 5 and 8 are co-prime, L.C.M. of 5 and 8 = 5 × 8 = 40.

Hence, option 3 is the correct option.

Every number (other than 0) has an infinite number of:

1. prime factors

2. factors

3. multiples

4. none of these

Answer

Every number (other than 0) has a finite number of factors but an infinite number of multiples.

Hence, option 3 is the correct option.

The value of 18 - (15 ÷ $\overline{12 - 9}$) is:

1. 13

2. 23

3. 1

4. none of these

Answer

By using BODMAS, we will solve in this order : Bracket, of, Division, Multiplication, Addition, Subtraction.

18 - (15 ÷ $\overline{12 - 9}$)

= 18 - (15 ÷ 3)

= 18 - $\dfrac{15}{3}$

= 18 - 5

= 13

Hence, option 1 is the correct option.

The number of common factors of 60 and 75 is:

1. 2

2. 3

3. 4

4. 1

Answer

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60

Factors of 75 = 1, 3, 5, 15, 25 and 75

Common factors of 60 and 75 = 1, 3, 5 and 15

The number of common factors = 4

Hence, option 3 is the correct option.

How many natural numbers have exactly one factor:

1. 0

2. 1

3. 2

4. none of these

Answer

Only the number 1 has exactly one factor, i.e. itself.

So, only 1 natural number has exactly one factor.

Hence, option 2 is the correct option.

Which of the following should be performed first to simplify the expression:

25 × 3 + (16 ÷ 4) - 10 ÷ 2 + 3

1. 25 × 3

2. 16 ÷ 4

3. 10 ÷ 2

4. 2 + 3

Answer

According to the order of operations (BODMAS), the operation inside the brackets should be performed first.

So, 16 ÷ 4 should be performed first.

Hence, option 2 is the correct option.

The HCF and the LCM of numbers 12 and 17 are respectively:

1. 1 and 17

2. 12 × 17 and 12 + 17

3. 12 and 1

4. 1 and 12 × 17

Answer

12 and 17 have no common factor other than 1, so they are co-prime.

⇒ H.C.F. of 12 and 17 = 1

⇒ L.C.M. of 12 and 17 = 12 × 17

Hence, option 4 is the correct option.

The L.C.M. of two numbers is 56 and their H.C.F. is 4, the product of the two numbers is:

1. 56

2. 56 ÷ 4

3. 56 × 4

4. none of these

Answer

We know that,

Product of two numbers = H.C.F. × L.C.M.

⇒ Product of two numbers = 4 × 56 = 56 × 4

Hence, option 3 is the correct option.

The H.C.F. and L.C.M. of 2 and 6 is:

1. 1 and 12

2. 1 and 6

3. 2 and 6

4. 2 and 12

Answer

2 = 2

6 = 2 × 3

H.C.F. = 2

L.C.M. = 2 × 3 = 6

Hence, option 3 is the correct option.

The H.C.F. and L.C.M. of 7 and 15 is :

1. 1 and 105

2. 7 and 75

3. 1 and 15

4. 1 and 7

Answer

7 and 15 have no common factor other than 1, so they are co-prime.

⇒ H.C.F. of 7 and 15 = 1

⇒ L.C.M. of 7 and 15 = 7 × 15 = 105

Hence, option 1 is the correct option.