Playing with Numbers Test

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Playing with Numbers Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

Find the greatest common factor of $$42,126$$ and $$210$$.

A
$$2$$

B
$$6$$

C
$$14$$

D
$$21$$

E
$$42$$

Solution

We know, $$42=2\times 3\times 7$$
$$126=2\times 3\times 3\times 7$$
$$210=2\times 3\times 5\times 7$$
$$\therefore$$ H.C.F $$=2\times 3\times 7=42$$
Question 2
1 / -0

Find the number of prime numbers between $$20$$ and $$40$$, both inclusive.

A
Three

B
Four

C
Five

D
Six

E
Seven

Solution

A number that is divisible by itself or $$1$$ is called prime number.
Prime number between $$20$$ and $$40$$ are $$23,29,31 ,37$$.
Then there are $$4$$ prime number between $$20$$ and $$40$$.
Question 3
1 / -0

What is the sum of the least prime number and the greatest negative even integer?

A
$$10$$

B
$$0$$

C
$$1$$

D
$$2$$

E
$$3$$

Solution

The least prime number is $$2$$, and the greatest negative even integer is $$-2$$, so the answer is $$0$$.
Question 4
1 / -0

What is the sum of the smallest prime and the largest prime less than $$10$$?

A
$$7$$

B
$$9$$

C
$$10$$

D
$$11$$

E
$$12$$

Solution

Smallest prime number less than $$10$$ is $$2$$ and largest prime number less than $$10$$ is $$7$$ and their sum is $$2+7=9$$
Question 5
1 / -0

What is the greatest common factor of $$45,135$$ and $$270$$?

A
$$5$$

B
$$9$$

C
$$15$$

D
$$25$$

E
$$45$$

Solution

The factors of the given numbers are:

$$45 = 1,3,5,9,15$$ and $$45$$
$$135 = 1,3,5,9,15,45$$ and $$135$$
$$270 = 1,3,5,9,15,45,90,135$$ and $$270$$

The common factors in each of the above numbers are $$3,3$$ and $$5$$.

Hence, the greatest common factor is $$3\times 3\times 5=45$$

and as $$45$$ is also a factor of both $$135$$ and $$270$$

Hence the GCF of $$45, 135$$ and $$270$$ is $$45$$
Question 6
1 / -0

Each of the following is a factor of $$80$$, except

A
$$5$$

B
$$8$$

C
$$12$$

D
$$16$$

E
$$40$$

Solution

The positive integers factor of $$80$$ are
$$1,2,4,5,8,10,20,40$$ and $$80$$
Then in given option the option C is $$12$$ not the factor a factor of $$80$$.
Answer is $$12$$.
Question 7
1 / -0

If the sum of the digits of a number is divisible by $$3$$, then the number is also divisible by __.

A
$$2$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

If the sum of the digits of a number is divisible by $$3$$, then the number is also divisible by $$3$$.
Example: $$372$$
Sum of the digits $$= 3 + 7 + 2 = 12,$$ which is divisible by $$3$$.
The number, $$372$$ is also divisible by $$3$$.
Question 8
1 / -0

How many numbers are divisible by $$9$$?
$$863, 267, 129, 774, 981, 997, 936$$

A
$$2$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

Here,
$$774=7+7+4=18, 981= 9+8+1=18, 936= 9+3+6=18$$ are divisible by $$9$$ because the sum of the digits of those numbers are a multiple of $$9$$.
Therefore, there are $$3$$ numbers divisible by $$9$$.

So, option B is correct.
Question 9
1 / -0

Find the highest common factor of $$36$$ and $$84$$.

A
$$4$$

B
$$6$$

C
$$12$$

D
$$18$$

Solution

Prime factors of $$36=2\times2\times3\times3$$
Prime Factors of $$84=2\times2\times 3\times 7$$
$$\therefore$$ H.C.F. $$=2\times2\times 3=12$$.
Question 10
1 / -0

How many prime numbers are less than $$50$$?

A
$$16$$

B
$$15$$

C
$$14$$

D
$$18$$

Solution

Prime numbers less than $$50$$ are:
$$2,3,5,7,11,13,17,19,23,29,31,37,41,43,47$$
Their number is $$15$$.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 16

Result

Playing with Numbers Test - 16

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Question 1

$$2$$

$$6$$

$$14$$

$$21$$

$$42$$

Solution

Question 2

Three

Four

Five

Six

Seven

Solution

Question 3

$$10$$

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 4

$$7$$

$$9$$

$$10$$

$$11$$

$$12$$

Solution

Question 5

$$5$$

$$9$$

$$15$$

$$25$$

$$45$$

Solution

Question 6

$$5$$

$$8$$

$$12$$

$$16$$

$$40$$

Solution

Question 7

$$2$$

$$3$$

$$4$$

$$5$$

Solution

Question 8

$$2$$

$$3$$

$$4$$

$$5$$

Solution

Question 9

$$4$$

$$6$$

$$12$$

$$18$$

Solution

Question 10

$$16$$

$$15$$

$$14$$

$$18$$

Solution

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