Playing with Numbers Test

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Playing with Numbers Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

H.C.F. of $$36$$ and $$144$$ is equal to :

A
$$36$$

B
$$144$$

C
$$4$$

D
$$2$$

Solution

Factors of $$36 = 2,2,3,3$$
Factors of $$144 = 2,2,2,2,3,3$$
Common factors of $$36$$ and $$144$$ are $$2,2,3,3$$
$$\therefore H.C.F = 2\times 2\times 3\times 3 = 36$$
Option A is correct.
Question 2
1 / -0

How many prime numbers are there between $$0$$ and $$30$$?

A
$$9$$

B
$$10$$

C
$$8$$

D
$$11$$

Solution

Prime numbers:- The numbers which are divisible by $$1$$ and themselves, or the number which has only two factors, $$1 $$ and the number itself
e.g. $$7$$
Note:- $$ 1$$ is not a prime number, the smallest prime number is $$2$$
Prime numbers between $$1$$ and $$30$$ are $$2,~3,~5,~7,~11,~13,~17,~19,~23,~29.$$
Total ten numbers are there.
Question 3
1 / -0

The resultant of "factor $$\times$$ factor $$ ......$$" is equal to

A
product

B
difference

C
sum

D
quotient

Solution

Let us consider two factors as $$2$$ and $$3$$

Then $$2\times 3=6$$

So, factor $$\times$$ factor $$=$$ Product
Question 4
1 / -0

Common factors of $$9$$ and $$36$$ are

A
$$1,3,9$$

B
$$1,4,3,5,9$$

C
$$1,4,5$$

D
none of these

Solution

Factors of $$ 9 = 1, 3, 9 $$
Factors of $$ 36 = 1, 3, 4, 6, 9, 12, 36 $$

Common factors are $$ 1, 3, 9 $$
Question 5
1 / -0

The number which is neither prime nor composite is

A
$$3$$

B
$$1$$

C
$$2$$

D
$$5$$

Solution

A prime number is a number which has only two factors, $$1$$ and the number itself. So, a prime number has 2 factors.
A composite number is a number that has factors other than $$1$$ and the number itself. A composite number has more than 2 factors.
The number which is neither prime nor composite is $$ 1 $$ as it is divisible only by $$1$$. It has only one factor.
Hence, Option B is correct answer.
Question 6
1 / -0

What is the remainder obtained when a prime number greater than $$6$$ is divided by $$6$$?

A
$$1 \ or\ 3$$

B
$$1 \ or\ 5$$

C
$$3\ or\ 5$$

D
$$4 \ or\ 5$$

Solution

We can take an example. Prime numbers greater than $$6$$ are $$7, 11, 13,$$ and so on. When $$7$$ is divided by $$6,$$ remainder is $$1$$. When $$11$$ is divided by $$6$$, remainder is $$5$$. Similarly, when $$13$$ is divided by $$6$$, remainder is $$1$$. The remainder obtained is either $$1$$ or $$5$$.
So the correct answer will be option $$B$$
Question 7
1 / -0

Number of prime numbers from 1 to 50 are

A
$$18$$

B
$$12$$

C
$$15$$

D
$$20$$

Solution

There are 15 prime numbers from 1 to 50. They are $$2, 3, 5, 7, 11, 13, 17,19, 23, 29, 31,37,41,43,47.$$
Question 8
1 / -0

All prime numbers are

A
even numbers

B
odd numbers

C
composite numbers

D
odd numbers except 2

Solution

Prime numbers are $$2,3,5,7,11,13,....$$

Only $$2$$ is an even number and others are odd numbers.

So, all prime numbers are odd numbers except for $$2$$.

Hence, correct answer is option D.
Question 9
1 / -0

Which of the following numbers are divisible by 2 but not by 4?

A
28

B
324

C
2356

D
8026

Solution

$$\Rightarrow$$ Divisibility by 2: Any even number or number whose last digit is an even number i.e. 2,4,6,8 including 0 is always completely divisible by 2.
$$\Rightarrow$$ Divisibility by 4: If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.
$$\Rightarrow$$ $$28,\,324$$ and $$2356$$ are divisible by both 2 and 4.
$$\Rightarrow$$ $$8026$$ contains last digit 6, so it is divisible by 2.
$$\Rightarrow$$ $$8026$$ last two digit is not divisible by 4.
$$\therefore$$ $$8026$$ is the number which is divisible by 2 but not 4.
Question 10
1 / -0

The prime number that comes just after 47 is ......

A
57

B
51

C
53

D
none of these

Solution

After $$47$$,
$$48,49,50,51,52$$ are composite numbers; but, $$53$$ is a prime number, as it has no factor other than 1 and itself.
So correct answer will be option C

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 8

Result

Playing with Numbers Test - 8

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SHARING IS CARING

Question 1

$$36$$

$$144$$

$$4$$

$$2$$

Solution

Question 2

$$9$$

$$10$$

$$8$$

$$11$$

Solution

Question 3

product

difference

sum

quotient

Solution

Question 4

$$1,3,9$$

$$1,4,3,5,9$$

$$1,4,5$$

none of these

Solution

Question 5

$$3$$

$$1$$

$$2$$

$$5$$

Solution

Question 6

$$1 \ or\ 3$$

$$1 \ or\ 5$$

$$3\ or\ 5$$

$$4 \ or\ 5$$

Solution

Question 7

$$18$$

$$12$$

$$15$$

$$20$$

Solution

Question 8

even numbers

odd numbers

composite numbers

odd numbers except 2

Solution

Question 9

28

324

2356

8026

Solution

Question 10

57

51

53

none of these

Solution

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